Toric Ideal Sheaves (Experimental)

Ideal sheaves on toric varieties are currently in experimental state. Currently, we support the following functionality. Note that, as of October 2023, this is limited to smooth toric varieties.

ideal_sheafMethod
ideal_sheaf(td::ToricDivisor)

Return the ideal sheaf corresponding to a toric divisor.

Examples

julia> P3 = projective_space(NormalToricVariety, 3)
Normal toric variety

julia> td = toric_divisor(P3, [0, 1, 0, 0])
Torus-invariant, prime divisor on a normal toric variety

julia> ideal_sheaf(td)
Sheaf of ideals
  on normal, smooth toric variety
with restrictions
  1: Ideal (x_2_1)
  2: Ideal (x_2_2)
  3: Ideal (1)
  4: Ideal (x_2_4)
Experimental

This function is part of the experimental code in Oscar. Please read here for more details.

source
ideal_sheafMethod
ideal_sheaf(X::NormalToricVariety, I::MPolyIdeal)

Create a sheaf of ideals on a toric variety $X$ from a homogeneous ideal I in its cox_ring.

Examples

julia> P3 = projective_space(NormalToricVariety, 3)
Normal toric variety

julia> (x1,x2,x3,x4) = gens(cox_ring(P3));

julia> I = ideal([x2,x3])
Ideal generated by
  x2
  x3

julia> IdealSheaf(P3, I);
Experimental

This function is part of the experimental code in Oscar. Please read here for more details.

source