Power Sums, Gorenstein Algebras,

and Determinantal Varieties

by A. Iarrobino and V. Kanev





Springer Lecture Notes in Mathematics #1721, 345+xxxi p.  (December,1999)






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. The next six chapters present the authors' recent work; the dominant theme of these chapters is 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. These chapters contain many concrete examples, some calculated with the aid of the computer algebra program ``Macaulay,'' which illustrate the abstract material. The final chapter considers open problems. The five appendices include one coauthored by Steven L. Kleiman on the Hilbert scheme. The book ends with an extensive bibliography, and with indices of subjects, names, and symbols. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. The only prerequisite is a basic knowledge of commutative algebra and algebraic geometry.

MATHEMATICS SUBJECT CLASSIFICATION NUMBERS (1991): 14M12 (determinantal varieties), 14C05 (parametrization), 13C40 (linkage, determinantal ideals), 14N99 (for "Classical problems"), 13H10 (Gorenstein rings).


Table of Contents

Preface

Short Description of Appendix: The Gotzmann Theorems and the Hilbert scheme (with S.L. Kleiman)

Directions to view or download Introduction or Chapter 1

drawing by Tony's Dad, for frontispiece of book



Errata

To contact the authors

Ordering (Springer)



AMS Math Review of book, by Juan Migliore (link to MathSciNet)  Copy. pdf dvi



A. Iarrobino web page

NU Math Dept web page

Created: October 15,1999. Last modified: January 19,2001
Comments to: iarrobin@neu.edu