© 1994

Kodaira-Spencer Maps in Local Algebra

  • Authors

Part of the Lecture Notes in Mathematics book series (LNM, volume 1597)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Bernd Herzog
    Pages 1-17
  3. Bernd Herzog
    Pages 18-29
  4. Bernd Herzog
    Pages 30-47
  5. Bernd Herzog
    Pages 48-58
  6. Bernd Herzog
    Pages 59-75
  7. Bernd Herzog
    Pages 76-90
  8. Bernd Herzog
    Pages 91-100
  9. Bernd Herzog
    Pages 101-126
  10. Bernd Herzog
    Pages 143-170
  11. Back Matter
    Pages 171-178

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.


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

Bibliographic information

  • Book Title Kodaira-Spencer Maps in Local Algebra
  • Authors Bernd Herzog
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-58790-3
  • eBook ISBN 978-3-540-49103-3
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages XVIII, 182
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
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