Cox rings and combinatorics

Abstract

For a variety with a finitely generated total coordinate ring, we describe basic geometric properties in terms of certain combinatorial structures living in its divisor class group. For example, we describe the singularities, we calculate the ample cone, and we give simple Fano criteria. As we show by means of several examples, these results allow explicit computations.

48 pages, final version, to appear in Transactions AMS

Cited by in corpus (2)

• GIT-equivalence beyond the ample cone
• On embeddings of homogeneous spaces with small boundary