LEADER 03467nam 2200625 450 001 996466651703316 005 20220211113557.0 010 $a3-540-46707-6 024 7 $a10.1007/BFb0093426 035 $a(CKB)1000000000437292 035 $a(SSID)ssj0000325780 035 $a(PQKBManifestationID)12087651 035 $a(PQKBTitleCode)TC0000325780 035 $a(PQKBWorkID)10253689 035 $a(PQKB)10482806 035 $a(DE-He213)978-3-540-46707-6 035 $a(MiAaPQ)EBC5578736 035 $a(Au-PeEL)EBL5578736 035 $a(OCoLC)1066198219 035 $a(MiAaPQ)EBC6866925 035 $a(Au-PeEL)EBL6866925 035 $a(PPN)15517777X 035 $a(EXLCZ)991000000000437292 100 $a20220211d1999 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aPower sums, Gorenstein algebras, and determinantal loci /$fAnthony Iarrobino, Vassil Kanev, S. L. Kleiman 205 $a1st ed. 1999. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1999] 210 4$dİ1999 215 $a1 online resource (XXXIV, 354 p.) 225 1 $aLecture Notes in Mathematics ;$v1721 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-66766-0 327 $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. 330 $aThis book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$vVolume 1721. 606 $aCatalecticant matrices 606 $aDeterminantal varieties 615 0$aCatalecticant matrices. 615 0$aDeterminantal varieties. 676 $a516.35 700 $aIarrobino$b Anthony$0478905 702 $aKanev$b Vassil$f1954- 702 $aKleiman$b S. L. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466651703316 996 $aPower Sums, Gorenstein Algebras, and Determinantal Loci$92514340 997 $aUNISA