Overview
- Authors:
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Manfred Herrmann
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Mathematisches Institut der Universität zu Köln, Köln 41, Germany
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Ulrich Orbanz
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Mathematisches Institut der Universität zu Köln, Köln 41, Germany
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Shin Ikeda
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Mathematical Department Gifu College of Education, Gifu, Japan
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Table of contents (9 chapters)
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Front Matter
Pages I-XVII
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- Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
Pages 1-43
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- Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
Pages 44-116
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- Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
Pages 117-151
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- Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
Pages 152-203
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- Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
Pages 204-239
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- Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
Pages 240-269
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- Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
Pages 270-325
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- Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
Pages 326-396
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- Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
Pages 397-446
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Back Matter
Pages 447-629
About this book
Content and Subject Matter: This research monograph deals with two main subjects, namely the notion of equimultiplicity and the algebraic study of various graded rings in relation to blowing ups. Both subjects are clearly motivated by their use in resolving singularities of algebraic varieties, for which one of the main tools consists in blowing up the variety along an equimultiple subvariety. For equimultiplicity a unified and self-contained treatment of earlier results of two of the authors is given, establishing a notion of equimultiplicity for situations other than the classical ones. For blowing up, new results are presented on the connection with generalized Cohen-Macaulay rings. To keep this part self-contained too, a section on local cohomology and local duality for graded rings and modules is included with detailed proofs. Finally, in an appendix, the notion of equimultiplicity for complex analytic spaces is given a geometric interpretation and its equivalence to the algebraic notion is explained. The book is primarily addressed to specialists in the subject but the self-contained and unified presentation of numerous earlier results make it accessible to graduate students with basic knowledge in commutative algebra.
