Literature constructions
Certain models have been studied in the physics literature over and over again. Thereby, these constructions became famous and some were given special names. We aim to provide support for such standard constructions. An example of such a model is the following:
su5_tate_model_over_arbitrary_3d_base — Methodsu5_tate_model_over_arbitrary_3d_base()Return the SU(5) Tate model over an arbitrary 3-dimensional base space. For more details see e.g. Timo Weigand (2018) and references therein.
julia> tm = su5_tate_model_over_arbitrary_3d_base()
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base
julia> v = ambient_space(tm)
Normal toric variety
julia> a10,a21,a32,a43,a65,w,x,y,z = gens(cox_ring(v));
julia> I = ideal([x,y,w]);
julia> v2 = domain(blow_up(v,I))
Normal toric variety
julia> cox_ring(v2)
Multivariate polynomial ring in 10 variables over QQ graded by
a10 -> [1 0 0 0]
a21 -> [0 1 0 0]
a32 -> [-1 2 0 0]
a43 -> [-2 3 0 0]
a65 -> [-4 5 0 0]
w -> [0 0 1 0]
x -> [0 1 1 2]
y -> [1 1 1 3]
z -> [0 0 0 1]
e -> [2 -1 -1 0]More generally, we support literature constructions.
literature_model — Methodliterature_model(; doi::String="", arxiv_id::String="", version="", equation::String="")Many models have been created in the F-theory literature. A significant number of them have even been given specific names, for instance the "U(1)-restricted SU(5)-GUT model". This method has access to a database, from which it can look up such literature models.
Currently, you can provide any combination of the following optional arguments to the method literature_model:
doi: A string representing the DOI of the publication that
introduced the model in question.
equation: A string representing the number of the equation that introduced
the model in question. For papers, that were posted on the arXiv, we can instead of the doi also provide the following:
arxiv_id: A string that represents the arXiv identifier of the paper that
introduced the model in question.
version: A string representing the version of the arXiv upload.
The method literature_model attempts to find a model in our database for which the provided data matches the information in our record. If no such model can be found, or multiple models exist with information matching the provided information, then an error is raised.
Some literature models require additional parameters to specified to single out a model from a family of models. Such models can be provided using the optional argument model_parameters, which should be a dictionary such as Dict("k" => 5).
julia> t = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> v = ambient_space(t)
Normal toric variety
julia> a1,a21,a32,a43,w,x,y,z = gens(cox_ring(v));
julia> I = ideal([x,y,w]);
julia> v2 = domain(blow_up(v, I))
Normal toric variety
julia> cox_ring(v2)
Multivariate polynomial ring in 9 variables over QQ graded by
a1 -> [1 0 0 0]
a21 -> [0 1 0 0]
a32 -> [-1 2 0 0]
a43 -> [-2 3 0 0]
w -> [0 0 1 0]
x -> [0 1 1 2]
y -> [1 1 1 3]
z -> [0 0 0 1]
e -> [2 -1 -1 0]Attributes
For literature models, we provide the following attributes:
arxiv_id — Methodarxiv_id(m::AbstractFTheoryModel)Return the arxiv_id of the preprint that introduced the given model. If no arxiv_id is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> arxiv_id(m)
"1109.3454"arxiv_doi — Methodarxiv_doi(m::AbstractFTheoryModel)Return the arxiv_doi of the preprint that introduced the given model. If no arxiv_doi is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> arxiv_doi(m)
"10.48550/arXiv.1109.3454"arxiv_link — Methodarxiv_link(m::AbstractFTheoryModel)Return the arxiv_link (formatted as string) to the arXiv version of the paper that introduced the given model. If no arxiv_link is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> arxiv_link(m)
"https://arxiv.org/abs/1109.3454v2"arxiv_model_equation_number — Methodarxiv_model_equation_number(m::AbstractFTheoryModel)Return the arxiv_model_equation_number in which the given model was introduced in the arXiv preprint in our record. If no arxiv_model_equation_number is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> arxiv_model_equation_number(m)
"3.1"arxiv_model_page — Methodarxiv_model_page(m::AbstractFTheoryModel)Return the arxiv_model_page on which the given model was introduced in the arXiv preprint in our record. If no arxiv_model_page is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> arxiv_model_page(m)
"10"arxiv_model_section — Methodarxiv_model_section(m::AbstractFTheoryModel)Return the arxiv_model_section in which the given model was introduced in the arXiv preprint in our record. If no arxiv_model_section is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> arxiv_model_section(m)
"3"arxiv_version — Methodarxiv_version(m::AbstractFTheoryModel)Return the arxiv_version of the arXiv preprint that introduced the given model. If no arxiv_version is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> arxiv_version(m)
"2"associated_literature_models — Methodassociated_literature_models(m::AbstractFTheoryModel)Return a list of the unique identifiers any associated_literature_models of the given model. These are either other presentations (Weierstrass, Tate, ...) of the given model, or other version of the same model from a different paper in the literature. If no associated_literature_models are known, an error is raised.
julia> m = literature_model(arxiv_id = "1507.05954", equation = "A.1")
Assuming that the first row of the given grading is the grading under Kbar
Weierstrass model over a not fully specified base -- U(1)xU(1) Weierstrass model based on arXiv paper 1507.05954 Eq. (A.1)
julia> associated_literature_models(m)
1-element Vector{String}:
"1507_05954-1"generating_sections — Methodgenerating_sections(m::AbstractFTheoryModel)Return a list of the known Mordell–Weil generating sections of the given model. If no generating sections are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> generating_sections(m)
1-element Vector{Vector{MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}}}:
[0, 0, 1]journal_doi — Methodjournal_doi(m::AbstractFTheoryModel)Return the journal_doi of the publication that introduced the given model. If no journal_doi is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> journal_doi(m)
"10.1016/j.nuclphysb.2011.12.013"journal_link — Methodjournal_link(m::AbstractFTheoryModel)Return the journal_link (formatted as string) to the published version of the paper that introduced the given model. If no journal_link is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> journal_link(m)
"https://www.sciencedirect.com/science/article/pii/S0550321311007115"journal_model_equation_number — Methodjournal_model_equation_number(m::AbstractFTheoryModel)Return the journal_model_equation_number in which the given model was introduced in the published paper in our record. If no journal_model_equation_number is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> journal_model_equation_number(m)
"3.1"journal_model_page — Methodjournal_model_page(m::AbstractFTheoryModel)Return the journal_model_page on which the given model was introduced in the published paper in our record. If no journal_model_page is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> journal_model_page(m)
"9"journal_model_section — Methodjournal_model_section(m::AbstractFTheoryModel)Return the journal_model_section in which the given model was introduced in the published paper in our record. If no journal_model_section is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> journal_model_section(m)
"3"journal_pages — Methodjournal_pages(m::AbstractFTheoryModel)Return the journal_pages of the published paper in which the given model was introduced. If no journal_pages are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> journal_pages(m)
"1–47"journal_report_numbers — Methodjournal_report_numbers(m::AbstractFTheoryModel)Return the journal_report_numbers of the published paper in which the given model was introduced. If no journal_report_numbers is known, an error is raised.
julia> m = literature_model(arxiv_id = "1507.05954", equation = "A.1")
Assuming that the first row of the given grading is the grading under Kbar
Weierstrass model over a not fully specified base -- U(1)xU(1) Weierstrass model based on arXiv paper 1507.05954 Eq. (A.1)
julia> journal_report_numbers(m)
3-element Vector{String}:
"UPR-1274-T"
"CERN-PH-TH-2015-157"
"MIT-CTP-4678"journal_volume — Methodjournal_volume(m::AbstractFTheoryModel)Return the journal_volume of the published paper in which the given model was introduced. If no journal_volume are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> journal_volume(m)
"858"journal_year — Methodjournal_year(m::AbstractFTheoryModel)Return the journal_year of the published paper in which the given model was introduced. If no journal_year is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> journal_year(m)
"2012"literature_identifier — Methodliterature_identifier(m::AbstractFTheoryModel)Return the literature_identifier of the given mode, which is a unique string that distinguishes the model from all others in the literature model database. If no literature_identifier is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> literature_identifier(m)
"1109_3454"model_description — Methodmodel_description(m::AbstractFTheoryModel)Return the model_description of the given model. If no model_description is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> model_description(m)
"SU(5)xU(1) restricted Tate model"model_parameters — Methodmodel_parameters(m::AbstractFTheoryModel)Return the model_parameters of the given model. If no model_parameters are known, an error is raised.
julia> m = literature_model(arxiv_id = "1212.2949", equation = "3.2", model_parameters = Dict("k" => 5))
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(2k+1) Tate model with parameter values (k = 5) based on arXiv paper 1212.2949 Eq. (3.2)
julia> model_parameters(m)
Dict{String, Int64} with 1 entry:
"k" => 5paper_authors — Methodpaper_authors(m::AbstractFTheoryModel)Return the paper_authors of the paper that introduced the given model. If no paper_authors are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> paper_authors(m)
3-element Vector{String}:
"Sven Krause"
"Christoph Mayrhofer"
"Timo Weigand"paper_buzzwords — Methodpaper_buzzwords(m::AbstractFTheoryModel)Return the paper_buzzwords of the paper that introduced the given model. If no paper_buzzwords are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> paper_buzzwords(m)
4-element Vector{String}:
"GUT model"
"Tate"
"U(1)"
"SU(5)"paper_description — Methodpaper_description(m::AbstractFTheoryModel)Return the paper_description of the paper that introduced the given model. If no paper_description is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> paper_description(m)
"SU(5)xU(1) restricted Tate model"paper_title — Methodpaper_title(m::AbstractFTheoryModel)Return the paper_title of the arXiv preprint that introduced the given model. If no paper_title is known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> paper_title(m)
"\$G_4\$ flux, chiral matter and singularity resolution in F-theory compactifications"related_literature_models — Methodrelated_literature_models(m::AbstractFTheoryModel)Return a list of the unique identifiers of any related_literature_models of the given model. These are models that are introduced in the same paper as the given model, but that are distinct from the given model. If no related_literature_models are known, an error is raised.
julia> m = literature_model(arxiv_id = "1212.2949", equation = "3.2", model_parameters = Dict("k" => 5))
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(2k+1) Tate model with parameter values (k = 5) based on arXiv paper 1212.2949 Eq. (3.2)
julia> related_literature_models(m)
6-element Vector{String}:
"1212_2949-2"
"1212_2949-3"
"1212_2949-4"
"1212_2949-5"
"1212_2949-6"
"1212_2949-7"resolutions — Methodresolutions(m::AbstractFTheoryModel)Return the list of all known resolutions for the given model. If no resolutions are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> resolutions(m)
1-element Vector{Vector{Vector}}:
[[["x", "y", "w"], ["y", "e1"], ["x", "e4"], ["y", "e2"], ["x", "y"]], ["e1", "e4", "e2", "e3", "s"]]resolution_generating_sections — Methodresolution_generating_sections(m::AbstractFTheoryModel)Return a list of lists of known Mordell–Weil generating sections for the given model after each known resolution. Each element of the outer list corresponds to a known resolution (in the same order), and each element of the list associated to a given resolution corresponds to a known generating section (in the same order). If no resolution generating sections are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> resolution_generating_sections(m)
1-element Vector{Vector{Vector{Vector{String}}}}:
[[["0", "0", "1"], ["0", "0", "1"], ["0", "1"], ["0", "1"], ["0", "1"], ["a32", "-a43"]]]resolution_zero_sections — Methodresolution_zero_sections(m::AbstractFTheoryModel)Return a list of known Mordell–Weil zero sections for the given model after each known resolution. Each element of the list corresponds to a known resolution (in the same order). If no resolution zero sections are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> resolution_zero_sections(m)
1-element Vector{Vector{Vector{String}}}:
[["1", "1", "0"], ["1", "1", "w"], ["1", "1"], ["1", "1"], ["1", "1"], ["1", "1"]]weighted_resolutions — Methodweighted_resolutions(m::AbstractFTheoryModel)Return the list of all known weighted resolutions for the given model. If no weighted resolutions are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> weighted_resolutions(m)
1-element Vector{Vector{Vector}}:
[Vector{Vector{Any}}[[["x", "y", "w"], [1, 1, 1]], [["x", "y", "w"], [1, 2, 1]], [["x", "y", "w"], [2, 2, 1]], [["x", "y", "w"], [2, 3, 1]], [["x", "y"], [1, 1]]], ["e1", "e4", "e2", "e3", "s"]]weighted_resolution_generating_sections — Methodweighted_resolution_generating_sections(m::AbstractFTheoryModel)Return a list of lists of known Mordell–Weil generating sections for the given model after each known weighted resolution. Each element of the outer list corresponds to a known weighted resolution (in the same order), and each element of the list associated to a given weighted resolution corresponds to a known generating section (in the same order). If no weighted resolution generating sections are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> weighted_resolution_generating_sections(m)
1-element Vector{Vector{Vector{Vector{String}}}}:
[[["0", "0", "1"], ["0", "0", "1"], ["0", "0", "1"], ["0", "0", "1"], ["0", "0", "1"], ["a32", "-a43"]]]weighted_resolution_zero_sections — Methodweighted_resolution_zero_sections(m::AbstractFTheoryModel)Return a list of known Mordell–Weil zero sections for the given model after each known weighted resolution. Each element of the list corresponds to a known weighted resolution (in the same order). If no weighted resolution zero sections are known, an error is raised.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> weighted_resolution_zero_sections(m)
1-element Vector{Vector{Vector{String}}}:
[["1", "1", "0"], ["1", "1", "w"], ["1", "1", "w"], ["1", "1", "w"], ["1", "1", "w"], ["1", "1"]]One can add this information for a model that does not have it:
set_description — Methodset_description(m::AbstractFTheoryModel, description::String)Set a description for a model.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> set_description(m, "An SU(5)xU(1) GUT-model")
julia> m
Global Tate model over a not fully specified base -- An SU(5)xU(1) GUT-model based on arXiv paper 1109.3454 Eq. (3.1)Note however, that these changes will (currently) not be stored in our data base. One can also check if a model has a particular set of information. This is achieved with the following methods:
has_arxiv_id(m::AbstractFTheoryModel),has_arxiv_doi(m::AbstractFTheoryModel),has_arxiv_link(m::AbstractFTheoryModel),has_arxiv_model_equation_number(m::AbstractFTheoryModel),has_arxiv_model_page(m::AbstractFTheoryModel),has_arxiv_model_section(m::AbstractFTheoryModel),has_arxiv_version(m::AbstractFTheoryModel),has_associated_literature_models(m::AbstractFTheoryModel),has_generating_sections(m::AbstractFTheoryModel),has_journal_doi(m::AbstractFTheoryModel),has_journal_link(m::AbstractFTheoryModel),has_journal_model_equation_number(m::AbstractFTheoryModel),has_journal_model_page(m::AbstractFTheoryModel),has_journal_model_section(m::AbstractFTheoryModel),has_journal_pages(m::AbstractFTheoryModel),has_journal_report_numbers(m::AbstractFTheoryModel),has_journal_volume(m::AbstractFTheoryModel),has_journal_year(m::AbstractFTheoryModel),has_literature_identifier(m::AbstractFTheoryModel),has_model_description(m::AbstractFTheoryModel),has_model_parameters(m::AbstractFTheoryModel),has_paper_authors(m::AbstractFTheoryModel),has_paper_buzzwords(m::AbstractFTheoryModel),has_paper_description(m::AbstractFTheoryModel),has_paper_title(m::AbstractFTheoryModel),has_related_literature_models(m::AbstractFTheoryModel),has_resolutions(m::AbstractFTheoryModel),has_resolution_generating_sections(m::AbstractFTheoryModel),has_resolution_zero_sections(m::AbstractFTheoryModel),has_weighted_resolutions(m::AbstractFTheoryModel),has_weighted_resolution_generating_sections(m::AbstractFTheoryModel),has_weighted_resolution_zero_sections(m::AbstractFTheoryModel),has_zero_section(m::AbstractFTheoryModel).
Methods
Resolution(s) of a singular model
A central task in F-theory is to resolve a singular model. For literature models, we have stored resolutions in our data base. Upon construction of a literature model, we load these known resolutions.
In addition to listing the known resolutions with resolutions(m::AbstractFTheoryModel), the user might want to add a resolution. This can be achieved with the following method:
add_resolution — Methodadd_resolution(m::AbstractFTheoryModel, centers::Vector{Vector{String}}, exceptionals::Vector{String})Add a known resolution for a model.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> add_resolution(m, [["x", "y"], ["y", "s", "w"], ["s", "e4"], ["s", "e3"], ["s", "e1"]], ["s", "w", "e3", "e1", "e2"])
julia> length(resolutions(m))
2Provided that a resolution for a model is known, we can (attempt to) resolve the model.
resolve — Methodresolve(m::AbstractFTheoryModel, index::Int)Resolve a model with the index-th resolution that is known.
Careful: Currently, this assumes that all blowups are toric blowups. We hope to remove this requirement in the near future.
julia> m = literature_model(arxiv_id = "1109.3454", equation = "3.1")
Assuming that the first row of the given grading is the grading under Kbar
Global Tate model over a not fully specified base -- SU(5)xU(1) restricted Tate model based on arXiv paper 1109.3454 Eq. (3.1)
julia> v = resolve(m, 1)
Normal toric variety
julia> cox_ring(v)
Multivariate polynomial ring in 13 variables over QQ graded by
a1 -> [1 0 0 0 0 0 0 0]
a21 -> [0 1 0 0 0 0 0 0]
a32 -> [-1 2 0 0 0 0 0 0]
a43 -> [-2 3 0 0 0 0 0 0]
w -> [0 0 1 0 0 0 0 0]
x -> [0 0 0 1 0 0 0 0]
y -> [0 0 0 0 1 0 0 0]
z -> [0 0 0 0 0 1 0 0]
e1 -> [0 0 0 0 0 0 1 0]
e4 -> [0 0 0 0 0 0 0 1]
e2 -> [1 -1 -1 -1 1 -1 -1 0]
e3 -> [1 0 0 1 -1 1 0 -1]
s -> [-2 2 2 -1 0 2 1 1]