rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Power sums, Gorenstein algebras, and determinantal loci
  name:
    name part: Iarrobino, Anthony A. (Anthony Ayers)
    name part: 1943-
    role:
      role term: creator
  name:
    name part: Kanev, Vassil
    name part: 1954-
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: gw
    date issued: 1999
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xxxi, 345 pages)
  abstract: 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: Introduction: Informal History and Brief Outline -- Catalecticant Varieties: Forms and Catalecticant Matrices. Sums of Powers and Linear Forms, and Gorenstein Algebras. Tangent Spaces to Catalecticant Schemes. The Locus PS(s, j;r) of Sums of Powers, and Determinantal Loci of Catalecticant Matrices -- Catalecticant Varieties and the Punctual Hilbert Scheme: Forms and Zero-Dimensional SchemesI: Basic Results, and the Case r = 3. Forms and Zero-Dimensional Schemes, II: Annihilating Schemes and Reducible Gor(T). Connectedness and Components of the Determinantal Locus PVs(u, v;r). Closures of the Variety Gor(T), and the Parameter Space G(T) of Graded Algebras -- Questions and Problems -- Appendix A: Divided Rings and Polynomial Rings -- Appendix B: Height Three Gorenstein Ideals -- Appendix C: The Gotzmann Theorems and the Hilbert Scheme (Anthony Iarrobino and S.L. Kleiman) -- Appendix D: Exemples of "Macaulay" Scripts -- Appendix E: Concordance with the 1996 Version.
  note: Anthony Iarrobino, Vassil Kanev.
  note: "With an appendix the Gotzmann Theorems and the Hilbert Scheme by Anthony Iarrobino and Steven L. Kleiman."
  note: Electronic resource.
  note: Includes bibliographical references (pages [319]-334) and indexes.
  subject:
    topic: Catalecticant matrices
  subject:
    topic: Determinantal varieties
  subject:
    topic: Hilbert schemes
  subject:
    topic: Catalecticant matrices
  subject:
    topic: Determinantal varieties
  subject:
    topic: Hilbert schemes
  classification: QA3 .L28 no. 1721
  classification: QA564
  classification: 510 s 516.3/5
  related item:
    title info:
      title: Power sums, Gorenstein algebras, and determinantal loci
    name:
      name part: Iarrobino, Anthony A. (Anthony Ayers), 1943-
    origin info:
      publisher: Berlin ; New York : Springer, ©1999
    identifier: (DLC) 99054164
    identifier: (OCoLC)42863051
  related item:
    title info:
      title: Lecture notes in mathematics (Springer-Verlag) ; 1721
  identifier: 9783540467076 (electronic bk.)
  identifier: 3540467076 (electronic bk.)
  identifier: 3540667660
  identifier: 9783540667667
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: COO
    record creation date: 991103
    record change date: 20260422203618.5
    record identifier: in00003509397
    language of cataloging:
      language term: eng