Power Sums, Gorenstein Algebras, and Determinantal Varieties
by A. Iarrobino and V. Kanev
Appendix: The Gotzmann Theorems and the Hilbert Scheme,
by A. Iarrobino and S. L. Kleiman.
to appear, Springer Lecture Notes #1721, 346+xxix pages, 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
Directions to download Introduction, Chapter 1
Short Description of Appendix: The Gotzmann Theorems and the Hilbert scheme (with
S.L. Kleiman)
drawing by Dad, for frontispiece of book
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