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. [BJRR10*1]),
  • vanishing sets of line bundle cohomology (cf. Appendix B of [Bie18]),
  • 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 [CLS11]. Our long term goals include the following:

  • Ensure that one can perform all computations of Appendix B in [CLS11].
  • Provide support for coherent sheaves and their sheaf cohomologies. In particular, the existing algorithms in ToricVarieties_project (based on [Bie18]) 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.