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The Cox Ring of a Del Pezzo Surface Has Rational Singularities

Oleg N. Popov
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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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Oleg N. Popov. 2004-02-10. The Cox Ring of a Del Pezzo Surface Has Rational Singularities. https://arxiv.org/abs/math/0402154

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