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Floer Cohomology and Flips

François Charest
Floer Cohomology and Flips by François Charest PDF

Author : François Charest
Publisher : American Mathematical Society
Page : 178 pages
File Size : 45,52 MB
Release : 2022-08-31
Category : Mathematics
ISBN : 147045310X

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Twenty-Four Hours of Local Cohomology

Srikanth B. Iyengar
Twenty-Four Hours of Local Cohomology by Srikanth B. Iyengar PDF

Author : Srikanth B. Iyengar
Publisher : American Mathematical Society
Page : 108 pages
File Size : 34,28 MB
Release : 2022-07-19
Category : Mathematics
ISBN : 1470471590

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This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.