Cox Rings and Combinatorics II

By Jürgen Hausen. 2008

65 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4d97ceacbef0ce3b1be8494fd5dcd1625c6c4d2f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Antonio Laface
2. M. Artebani
3. Jürgen Hausen

In Electrical and Electronic Engineering

1. Antonio Laface
2. M. Artebani

In Geometry and Topology

1. Antonio Laface
2. M. Artebani
3. Jürgen Hausen
4. D. Huybrechts
5. Shinnosuke Okawa
6. Hendrik Suss

Citations in the corpus

• On Cox rings of K3 surfaces (2009, methodology): “If Cl(X) has torsion, then the unique factorization property is replaced by a graded version: every nontrivial homogeneous nonunit is a product of homogeneous primes, where the latter refers to nontrivial homogeneous nonunits f such that f |gh with g, h homogeneous implies f |g or f |h, see [12].”