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...

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Published in:arXiv.org 2004-12
Main Authors: Berchtold, Florian, Hausen, Juergen
Format: Article
Language:English
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Combinatorial analysis
Singularities
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Hausen, Juergen
description 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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subjects Combinatorial analysis
Singularities
title Cox rings and combinatorics
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