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26 April 2024 |
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An Introduction to Tight Closure | Karen E. Smith
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26 Sep 2002 | Journal: | in: Geometric and combinatorial aspects of commutative algebra (Messina, 1999), 353--377, Lecture Notes in Pure and Appl. Math., 217, Dekker, New York, 2001 | Subject: | Commutative Algebra; Algebraic Geometry MSC-class: 13A35; 13D45 14B05 14C20 14F17 | math.AC math.AG | Abstract: | 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. | Source: | arXiv, math.AC/0209378 | Services: | Forum | Review | PDF | Favorites |
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