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. (2010)),
  • vanishing sets of line bundle cohomology (cf. Appendix B of 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.

Long term goals

We follow David A. Cox, John B. Little, Henry K. Schenck (2011). Our long term goals include the following:


Please direct questions about this part of OSCAR to the following people: