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  • Book
  • © 1994

Kodaira-Spencer Maps in Local Algebra

Authors:

  1. Bernd Herzog
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1597)

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  • ISBN: 978-3-540-49103-3
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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XVII
    PDF

  2. Ring filtrations

    • Bernd Herzog
    Pages 1-17

  3. Basic lemmas

    • Bernd Herzog
    Pages 18-29

  4. Tangential flatness under base change

    • Bernd Herzog
    Pages 30-47

  5. Relation to flatness

    • Bernd Herzog
    Pages 48-58

  6. Distinguished bases

    • Bernd Herzog
    Pages 59-75

  7. Hilbert series

    • Bernd Herzog
    Pages 76-90

  8. Flatifying filtrations

    • Bernd Herzog
    Pages 91-100

  9. Kodaira-Spencer maps

    • Bernd Herzog
    Pages 101-126

  11. On the local rings of the Hilbert scheme

    • Bernd Herzog
    Pages 143-170

  12. Back Matter

    Pages 171-178
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About this book

The monograph contributes to Lech's inequality - a 30-year-old problem of commutative algebra, originating in the work of Serre and Nagata, that relates the Hilbert function of the total space of an algebraic or analytic deformation germ to the Hilbert function of the parameter space.
A weakened version of Lech's inequality is proved using a construction that can be considered as a local analog of the Kodaira-Spencer map known from the deformation theory of compact complex manifolds. The methods are quite elementary, and will be of interest for researchers in deformation theory, local singularities and Hilbert functions.
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Keywords

  • Hilbert series
  • Kodaira-Spencer map
  • algebra
  • deformation germ
  • flatification
  • ring filtration
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Bibliographic Information

  • Book Title: Kodaira-Spencer Maps in Local Algebra

  • Authors: Bernd Herzog

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0074026

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-58790-3Published: 16 December 1994

  • eBook ISBN: 978-3-540-49103-3Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVIII, 182

  • Topics: Algebra

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Access via your institution
eBook USD 29.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-49103-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 39.95
Price excludes VAT (USA)
Learn about institutional subscriptions