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The Cox Ring of a Del Pezzo Surface Has Rational Singularities

2004/02/10 by Oleg N. Popov, О. Н. Попов, Popov, Oleg N.
Mathematics · Physics and Astronomy · #14J17 #14J26 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14J17 #msc:14J26

paper · pdf · doi:10.48550/arxiv.math/0402154

12 pages, LateX, uses XY-Pic

arxiv created 2004/02/10 · openalex publication_date 2004/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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