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＜電子ブック＞
Power Sums, Gorenstein Algebras, and Determinantal Loci / by Anthony Iarrobino, Vassil Kanev
(Lecture Notes in Mathematics. ISSN:16179692 ; 1721)

版	1st ed. 1999.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1999
本文言語	英語
大きさ	XXXIV, 354 p : online resource
冊子体	Power sums, Gorenstein algebras, and determinantal loci / Anthony Iarrobino, Vassil Kanev
著者標目	*Iarrobino, Anthony author Kanev, Vassil author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Associative rings LCSH:Associative algebras FREE:Algebraic Geometry FREE:Associative Rings and Algebras
一般注記	Forms 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 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/BFb0093426

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