The Cox Ring of a Del Pezzo Surface Has Rational Singularities
Algebraic Geometry
2007-05-23 v1
Abstract
For a smooth Del Pezzo surface the direct sum of global sections of all isomorphism classes of invertible sheaves on it can be almost canonically endowed with a ring structure, called the Cox ring. We show that in characteristic 0 this ring is Gorenstein and its spectrum has rational singularities. Also a gap in math.AG/0309111 is pointed out.
Cite
@article{arxiv.math/0402154,
title = {The Cox Ring of a Del Pezzo Surface Has Rational Singularities},
author = {Oleg N. Popov},
journal= {arXiv preprint arXiv:math/0402154},
year = {2007}
}
Comments
12 pages, LateX, uses XY-Pic