An Introduction to Tight Closure

Details An Introduction to Tight Closure An Introduction to Tight Closure

2002-09-26

arxiv.org/abs/math/0209378v1

in: Geometric and combinatorial aspects of commutative algebra (Messina, 1999), 353--377, Lecture Notes in Pure and Appl. Math

Mathematics

Commutative Algebra

latex. 25 pages. Lecture notes from lectures given in Messina Italy and Kashikojima Japan

Scientific paper

This is an expanded version of the author's lecture at the Conference in Commutative Algebra and Algebraic Geometry in Messina Italy in June 1999. The purpose of the talk was to give a brief introduction to the subject of tight closure, aimed at commutative algebraists who have not before studied this topic. The first part focused mainly on the definition and basic properties, with the second part focusing on some applications to algebraic geometry, particularly to global generation of adjoint linear series. These lecture notes follow even more closely a series of two lectures I gave in Kashikojima, Japan, at the Twentieth Annual Japanese Conference in Commutative Algebra the previous fall, and were distributed also in conjunction with that conference.

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