Tight closure and plus closure in dimension two

2004/02/11 by Holger Brenner, Brenner, Holger
Mathematics · #13A35 #14H60 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13A35 #msc:14H60

paper · pdf · doi:10.48550/arxiv.math/0402179

Some minor changes. To appear in Amer. J. of Math

arxiv created 2005/01/25 · arxiv updated 2009/12/01

Abstract

We prove that the tight closure and the graded plus closure of a homogeneous ideal coincide for a two-dimensional N-graded domain of finite type over the algebraic closure of a finite field. This answers in this case a ``tantalizing question'' of Hochster.

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