Cox rings and combinatorics
Algebraic Geometry
2007-05-23 v3
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.
Cite
@article{arxiv.math/0311105,
title = {Cox rings and combinatorics},
author = {Florian Berchtold and Juergen Hausen},
journal= {arXiv preprint arXiv:math/0311105},
year = {2007}
}
Comments
48 pages, final version, to appear in Transactions AMS