The Cox Ring of a Del Pezzo Surface Has Rational Singularities

Details The Cox Ring of a Del Pezzo Surface Has Rational Singularities The Cox Ring of a Del Pezzo Surface Has Rational Singularities

2004-02-10

arxiv.org/abs/math/0402154v1

Mathematics

Algebraic Geometry

12 pages, LateX, uses XY-Pic

Scientific paper

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.

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