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Cox rings and combinatorics II

Authors
  • Hausen, Juergen
Type
Published Article
Publication Date
Sep 04, 2008
Submission Date
Jan 25, 2008
Source
arXiv
License
Yellow
External links

Abstract

We study varieties with a finitely generated Cox ring. In a first part, we generalize a combinatorial approach developed in earlier work for varieties with a torsion free divisor class group to the case of torsion. Then we turn to modifications, e.g., blow ups, and the question how the Cox ring changes under such maps. We answer this question for a certain class of modifications induced from modifications of ambient toric varieties. Moreover, we show that every variety with finitely generated Cox ring can be explicitly constructed in a finite series of toric ambient modifications from a combinatorially minimal one.

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