Cox rings of degree one del Pezzo surfaces

Details Cox rings of degree one del Pezzo surfaces Cox rings of degree one del Pezzo surfaces

2008-03-03

arxiv.org/abs/0803.0353v2

Algebra and Number Theory 3 (2009) 729-761.

Mathematics

Algebraic Geometry

Significant revision. Proposition 4.4 fixes gap in previous version. To appear in Algebra and Number Theory

Scientific paper

Let X be a del Pezzo surface of degree one over an algebraically closed field (of any characteristic), 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.

Affiliated with

Also associated with

No associations

Rating

Cox rings of degree one del Pezzo surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cox rings of degree one del Pezzo surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cox rings of degree one del Pezzo surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-405644