Power Sums, Gorenstein Algebras, and Determinantal Loci

  • Authors
  • Anthony Iarrobino
  • Vassil Kanev

Part of the Lecture Notes in Mathematics book series (LNM, volume 1721)

Table of contents

  1. Front Matter
    Pages I-XXXI
  2. Anthony Iarrobino, Vassil Kanev
    Pages 3-56
  3. Anthony Iarrobino, Vassil Kanev
    Pages 57-72
  4. Anthony Iarrobino, Vassil Kanev
    Pages 73-90
  5. Anthony Iarrobino, Vassil Kanev
    Pages 131-205
  6. Anthony Iarrobino, Vassil Kanev
    Pages 237-247
  7. Anthony Iarrobino, Vassil Kanev
    Pages 255-264
  8. Back Matter
    Pages 265-346

About this book

Introduction

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.

Keywords

Dimension Grad algebra algebraic geometry commutative algebra

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0093426
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-66766-7
  • Online ISBN 978-3-540-46707-6
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book