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Cox rings of degree one del Pezzo surfaces
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Testa, Damiano, Várilly-Alvarado, Anthony and Velasco, Mauricio (2009) Cox rings of degree one del Pezzo surfaces. Algebra & Number Theory, Vol.3 (No.7). pp. 729-761. doi:10.2140/ant.2009.3.729
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Official URL: http://dx.doi.org/10.2140/ant.2009.3.729
Abstract
Let X be a del Pezzo surface of degree one over an algebraically closed field, and let Cox(X) be its total coordinate ring. We prove the missing case of a conjecture of Batyrev and Popov, which states that Cox(X) is a quadratic algebra. We use a complex of vector spaces whose homology determines part of the structure of the minimal free Pic(X)-graded resolution of Cox(X) over a polynomial ring. We show that sufficiently many Betti numbers of this minimal free resolution vanish to establish the conjecture.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Algebra & Number Theory | ||||
| Publisher: | Mathematical Sciences Publishers | ||||
| ISSN: | 1937-0652 | ||||
| Official Date: | 29 November 2009 | ||||
| Dates: |
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| Volume: | Vol.3 | ||||
| Number: | No.7 | ||||
| Page Range: | pp. 729-761 | ||||
| DOI: | 10.2140/ant.2009.3.729 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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