Algebra & Number Theory
- Algebra Number Theory
- Volume 3, Number 7 (2009), 729-761.
Cox rings of degree one del Pezzo surfaces
Let be a del Pezzo surface of degree one over an algebraically closed field, and let be its total coordinate ring. We prove the missing case of a conjecture of Batyrev and Popov, which states that is a quadratic algebra. We use a complex of vector spaces whose homology determines part of the structure of the minimal free -graded resolution of over a polynomial ring. We show that sufficiently many Betti numbers of this minimal free resolution vanish to establish the conjecture.
Algebra Number Theory, Volume 3, Number 7 (2009), 729-761.
Received: 8 March 2008
Revised: 5 June 2009
Accepted: 14 September 2009
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14J26: Rational and ruled surfaces
Testa, Damiano; Várilly-Alvarado, Anthony; Velasco, Mauricio. Cox rings of degree one del Pezzo surfaces. Algebra Number Theory 3 (2009), no. 7, 729--761. doi:10.2140/ant.2009.3.729. https://projecteuclid.org/euclid.ant/1513797480