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Power Sums, Gorenstein Algebras, and Determinantal Loci

  • Book
  • © 1999

Overview

Authors:
  1. Anthony Iarrobino
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  2. Vassil Kanev
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1721)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XXXI
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  2. Forms and catalecticant matrices

    • Anthony Iarrobino, Vassil Kanev
    Pages 3-56

  3. Sums of powers of linear forms, and gorenstein algebras

    • Anthony Iarrobino, Vassil Kanev
    Pages 57-72

  4. Tangent spaces to catalecticant schemes

    • Anthony Iarrobino, Vassil Kanev
    Pages 73-90

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

    • Anthony Iarrobino, Vassil Kanev
    Pages 91-127

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

    • Anthony Iarrobino, Vassil Kanev
    Pages 131-205

  7. Forms and zero-dimensional schemes, II: Annihilating schemes and reducible Gor(T)

    • Anthony Iarrobino, Vassil Kanev
    Pages 207-236

  8. Connectedness and components of the determinantal locus ℙV s(u, v; r)

    • Anthony Iarrobino, Vassil Kanev
    Pages 237-247

  9. Closures of the variety Gor(T), and the parameter space G(T) of graded algebras

    • Anthony Iarrobino, Vassil Kanev
    Pages 249-253

  10. Questions and problems

    • Anthony Iarrobino, Vassil Kanev
    Pages 255-264

  11. Back Matter

    Pages 265-346
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Keywords

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.

Bibliographic Information

  • Book Title: Power Sums, Gorenstein Algebras, and Determinantal Loci

  • Authors: Anthony Iarrobino, Vassil Kanev

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093426

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-540-66766-7Published: 15 December 1999

  • eBook ISBN: 978-3-540-46707-6Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XXXIV, 354

  • Topics: Algebraic Geometry, Associative Rings and Algebras

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