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Overview"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." Full Product DetailsAuthor: A. Iarrobino , Anthony Iarrobino , S.L. Kleiman , Vassil KanevPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 1999 ed. Volume: 1721 Dimensions: Width: 15.50cm , Height: 2.00cm , Length: 23.50cm Weight: 1.200kg ISBN: 9783540667667ISBN 10: 3540667660 Pages: 354 Publication Date: 15 December 1999 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsForms and catalecticant matrices.- Sums of powers of 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.- Forms and zero-dimensional schemes I: 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 ?V s(u, v; r).- Closures of the variety Gor(T), and the parameter space G(T) of graded algebras.- Questions and problems.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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