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2009 Cox rings of degree one del Pezzo surfaces
Damiano Testa, Anthony Várilly-Alvarado, Mauricio Velasco
Algebra Number Theory 3(7): 729-761 (2009). DOI: 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.

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Damiano Testa. Anthony Várilly-Alvarado. Mauricio Velasco. "Cox rings of degree one del Pezzo surfaces." Algebra Number Theory 3 (7) 729 - 761, 2009. https://doi.org/10.2140/ant.2009.3.729

Information

Received: 8 March 2008; Revised: 5 June 2009; Accepted: 14 September 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1191.14047
MathSciNet: MR2579393
Digital Object Identifier: 10.2140/ant.2009.3.729

Subjects:
Primary: 14J26

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.3 • No. 7 • 2009
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