# Introduction

## Content

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.

## Status

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: