Lecture Notes in Mathematics

Power Sums, Gorenstein Algebras, and Determinantal Loci

Authors: Iarrobino, Anthony, Kanev, Vassil

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About this book

This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry.

Table of contents (9 chapters)

  • Forms and catalecticant matrices

    Iarrobino, Anthony (et al.)

    Pages 3-56

  • Sums of powers of linear forms, and gorenstein algebras

    Iarrobino, Anthony (et al.)

    Pages 57-72

  • Tangent spaces to catalecticant schemes

    Iarrobino, Anthony (et al.)

    Pages 73-90

  • The locus PS(s, j; r) of sums of powers, and determinantal loci of catalecticant matrices

    Iarrobino, Anthony (et al.)

    Pages 91-127

  • Forms and zero-dimensional schemes I: Basic results, and the case r=3

    Iarrobino, Anthony (et al.)

    Pages 131-205

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-540-46707-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $79.95
price for USA
  • ISBN 978-3-540-66766-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Power Sums, Gorenstein Algebras, and Determinantal Loci
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1721
Copyright
1999
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-46707-6
DOI
10.1007/BFb0093426
Softcover ISBN
978-3-540-66766-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXXIV, 354
Topics