Tight closure and plus closure in dimension two

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.

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

Cited by in corpus (2)

• The rationality of the Hilbert-Kunz multiplicity in graded dimension two
• A Hilbert-Kunz criterion for solid closure in dimension two (characteristic zero)