Power Sums, Gorenstein Algebras, and Determinantal Loci
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...
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| Auteurs principaux: | , , |
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| Format: | Livre numérique |
| Sprog: | Anglais |
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Berlin [etc.] :
Springer
[20..].
Cham : Springer Nature |
| Serier: | Lecture notes in mathematics
1721 |
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Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Power sums, Gorenstein algebras, and determinantal loci, Anthony Iarrobino, Vassil Kanev, by Anthony Iarrobino and Steven L. Kleiman, 1999, Berlin, Springer, 1 vol. (XXXI-345 p.), Lecture notes in mathematics, 3-540-66766-0 • Power Sums, Gorenstein Algebras, and Determinantal Loci, Texte imprimé, 9783662214862 |
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| 020 | |a 9783540467076 (PDF) | ||
| 041 | 0 | |a eng | |
| 082 | |a 512.5 | ||
| 082 | |a 510 | ||
| 100 | 1 | |a Iarrobino, Anthony A., |d 1943- | |
| 245 | 1 | 0 | |a Power Sums, Gorenstein Algebras, and Determinantal Loci |c Anthony Iarrobino, Vassil Kanev. The Gotzmann theorems and the Hilbert scheme / by Anthony Iarrobino and Steven L. Kleiman. |
| 260 | |a Berlin [etc.] : |b Springer. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Lecture notes in mathematics |v 1721 |x 1617-9692 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. | ||
| 650 | |a Schémas de Hilbert | ||
| 650 | |a Variétés algébriques | ||
| 650 | |a Matrices | ||
| 650 | |a Géométrie algébrique | ||
| 650 | |a Mathématiques | ||
| 650 | |a Anneaux associatifs | ||
| 700 | 1 | |a Kleiman, Steven Lawrence, |d 1942- |4 aut | |
| 700 | 1 | |a Kanev, Vassil, |d 1954- |4 aut | |
| 776 | 0 | |0 061624772 |t Power sums, Gorenstein algebras, and determinantal loci |f Anthony Iarrobino, Vassil Kanev |f by Anthony Iarrobino and Steven L. Kleiman |d 1999 |c Berlin |n Springer |p 1 vol. (XXXI-345 p.) |s Lecture notes in mathematics |z 3-540-66766-0 | |
| 776 | 0 | |t Power Sums, Gorenstein Algebras, and Determinantal Loci |b Texte imprimé |z 9783662214862 | |
| 777 | 0 | |t The Gotzmann theorems and the Hilbert scheme |f by Anthony Iarrobino and Steven L. Kleiman | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/BFb0093426 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-WQ0L8756-S |z Accès sur la plateforme Istex | |
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| 997 | |0 969682 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||