Cox rings and combinatorics

Details Cox rings and combinatorics Cox rings and combinatorics

2003-11-07

arxiv.org/abs/math/0311105v3

Transactions AMS, Vol. 359, No. 3, 1205-1252 (2007)

Mathematics

Algebraic Geometry

48 pages, final version, to appear in Transactions AMS

Scientific paper

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.

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