The toric geometry part of OSCAR comprises algorithms addressing normal toric varieties and objects from commutative algebra and polyhedral geometry derived thereof. In particular, we provide support for the following:
- torus-invariant divisor (classes),
- line bundles,
- line bundle cohomology via
cohomCalg(cf. Ralph Blumenhagen, Benjamin Jurke, Thorsten Rahn, Helmut Roschy (2010)),
- vanishing sets of line bundle cohomology (cf.
Appendix Bof Martin Bies (2018)),
- cohomology ring and cohomology classes,
- Chow ring, algebraic cycles and intersection theory,
- elementary support for closed subvarieties.
This project is work-in-progress.
We provide a tutorial for toric geometry in OSCAR.
Long term goals
We follow David A. Cox, John B. Little, Henry K. Schenck (2011). Our long term goals include the following:
- Ensure that one can perform all computations of
Appendix Bin David A. Cox, John B. Little, Henry K. Schenck (2011).
- Provide support for coherent sheaves and their sheaf cohomologies. In particular, the existing algorithms in ToricVarieties_project (based on Martin Bies (2018)) should eventually be available in OSCAR.
Please direct questions about this part of OSCAR to the following people:
You can ask questions in the OSCAR Slack.
Alternatively, you can raise an issue on github.