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Equimultiplicity and Blowing Up

An Algebraic Study

  • Manfred Herrmann
  • Ulrich Orbanz
  • Shin Ikeda

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
    Pages 1-43
  3. Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
    Pages 44-116
  4. Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
    Pages 117-151
  5. Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
    Pages 152-203
  6. Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
    Pages 204-239
  7. Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
    Pages 240-269
  8. Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
    Pages 270-325
  9. Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
    Pages 326-396
  10. Manfred Herrmann, Ulrich Orbanz, Shin Ikeda
    Pages 397-446
  11. Back Matter
    Pages 447-629

About this book

Introduction

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.

Keywords

Blowing up Dimension Divisor Equivalence Grad Grothendieck topology algebra algebraic varieties cohomology commutative property duality knowledge proof sheaves tool

Authors and affiliations

  • Manfred Herrmann
    • 1
  • Ulrich Orbanz
    • 1
  • Shin Ikeda
    • 2
  1. 1.Mathematisches Institut der Universität zu KölnKöln 41Germany
  2. 2.Mathematical Department Gifu College of EducationGifuJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-61349-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-64803-8
  • Online ISBN 978-3-642-61349-4
  • Buy this book on publisher's site