000 | 03442nam a22004935i 4500 | ||
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001 | 978-3-540-46707-6 | ||
003 | DE-He213 | ||
005 | 20190213151238.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s1999 gw | s |||| 0|eng d | ||
020 |
_a9783540467076 _9978-3-540-46707-6 |
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024 | 7 |
_a10.1007/BFb0093426 _2doi |
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050 | 4 | _aQA564-609 | |
072 | 7 |
_aPBMW _2bicssc |
|
072 | 7 |
_aMAT012010 _2bisacsh |
|
072 | 7 |
_aPBMW _2thema |
|
082 | 0 | 4 |
_a516.35 _223 |
100 | 1 |
_aIarrobino, Anthony. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_aPower Sums, Gorenstein Algebras, and Determinantal Loci _h[electronic resource] / _cby Anthony Iarrobino, Vassil Kanev. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1999. |
|
300 |
_aXXXIV, 354 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
||
490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1721 |
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505 | 0 | _aForms 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. | |
520 | _aThis 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 | 0 | _aGeometry, algebraic. | |
650 | 0 | _aAlgebra. | |
650 | 1 | 4 |
_aAlgebraic Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M11019 |
650 | 2 | 4 |
_aAssociative Rings and Algebras. _0http://scigraph.springernature.com/things/product-market-codes/M11027 |
700 | 1 |
_aKanev, Vassil. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783662214862 |
776 | 0 | 8 |
_iPrinted edition: _z9783540667667 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1721 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0093426 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
_c10014 _d10014 |