Picard-graded Betti numbers and the defining ideals of Cox rings

Antonio Laface, Mauricio Velasco

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We introduce a complex of vector spaces whose homology determines the Picard-graded Betti numbers of the Cox ring of a Mori Dream Space. As an application of this construction we prove a conjecture of Batyrev and Popov which describes presentations for the Cox rings of Del Pezzo surfaces of degree at least two.

Original languageEnglish
Pages (from-to)353-372
Number of pages20
JournalJournal of Algebra
Volume322
Issue number2
DOIs
StatePublished - 15 Jul 2009
Externally publishedYes

Keywords

  • Cox rings
  • Del Pezzo surfaces
  • Multigraded Betti numbers

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