Cox rings and combinatorics

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...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2004-12
Main Authors: Berchtold, Florian, Hausen, Juergen
Format: Article
Language:English
Subjects:
Combinatorial analysis
Singularities
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422