Descript 
1 online resource (xxxi, 345 p.) 
Series 
Lecture notes in mathematics, 00758434 ; 1721


Lecture notes in mathematics (SpringerVerlag) ; 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 ZeroDimensional SchemesI: Basic Results, and the Case r = 3. Forms and ZeroDimensional 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 GorensteinArtin algebras, and of Hilbert schemes of zerodimensional 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

