Author Iarrobino, Anthony A. (Anthony Ayers), 1943-
Title Power sums, Gorenstein algebras, and determinantal loci [electronic resource] / Anthony Iarrobino, Vassil Kanev
Imprint Berlin ; New York : Springer, c1999
book jacket
Descript 1 online resource (xxxi, 345 p.)
Series Lecture notes in mathematics, 0075-8434 ; 1721
Lecture notes in mathematics (Springer-Verlag) ; 1721
Note "With an appendix the Gotzmann Theorems and the Hilbert Scheme by Anthony Iarrobino and Steven L. Kleiman."
Includes bibliographical references (p. [319]-334) and indexes
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
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
Link Print version: Iarrobino, Anthony A. (Anthony Ayers), 1943- Power sums, Gorenstein algebras, and determinantal loci. Berlin ; New York : Springer, c1999 3540667660 (DLC) 99054164 (OCoLC)42863051
Subject Catalecticant matrices
Determinantal varieties
Hilbert schemes
Catalecticant matrices. fast (OCoLC)fst00848646
Determinantal varieties. fast (OCoLC)fst00891647
Hilbert schemes. fast (OCoLC)fst00956784
Electronic books
Alt Author Kanev, Vassil, 1954-