LEADER 00000cam  22005414a 4500 
001    162121475 
003    OCoLC 
005    20140223021610.0 
006    m     o  d         
007    cr |n||||||||| 
008    991103s1999    gw      ob    001 0 eng c 
020    9783540467076 (electronic bk.) 
020    3540467076 (electronic bk.) 
035    (OCoLC)162121475|z(OCoLC)686119283|z(OCoLC)771199990 
042    pcc 
050  4 QA3|b.L28 no. 1721|aQA564 
082 04 510 s|a516.3/5|221 
100 1  Iarrobino, Anthony A.|q(Anthony Ayers),|d1943- 
245 10 Power sums, Gorenstein algebras, and determinantal loci
       |h[electronic resource] /|cAnthony Iarrobino, Vassil Kanev
260    Berlin ;|aNew York :|bSpringer,|cc1999 
300    1 online resource (xxxi, 345 p.) 
490 1  Lecture notes in mathematics,|x0075-8434 ;|v1721 
500    "With an appendix the Gotzmann Theorems and the Hilbert 
       Scheme by Anthony Iarrobino and Steven L. Kleiman." 
504    Includes bibliographical references (p. [319]-334) and 
505 0  Introduction: Informal History and Brief Outline -- 
       Catalecticant Varieties: Forms and Catalecticant Matrices.
       Sums of Powers and 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 -- Catalecticant Varieties and the 
       Punctual Hilbert Scheme: Forms and Zero-Dimensional 
       SchemesI: 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 PVs(u,v;r). Closures of the Variety 
       Gor(T), and the Parameter Space G(T) of Graded Algebras --
       Questions and Problems -- Appendix A: Divided Rings and 
       Polynomial Rings -- Appendix B: Height Three Gorenstein 
       Ideals -- Appendix C: The Gotzmann Theorems and the 
       Hilbert Scheme (Anthony Iarrobino and S.L. Kleiman) -- 
       Appendix D: Exemples of "Macaulay" Scripts -- Appendix E: 
       Concordance with the 1996 Version 
520    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 
650  0 Catalecticant matrices 
650  0 Determinantal varieties 
650  0 Hilbert schemes 
650  7 Catalecticant matrices.|2fast|0(OCoLC)fst00848646 
650  7 Determinantal varieties.|2fast|0(OCoLC)fst00891647 
650  7 Hilbert schemes.|2fast|0(OCoLC)fst00956784 
655  4 Electronic books 
700 1  Kanev, Vassil,|d1954- 
776 08 |iPrint version:|aIarrobino, Anthony A. (Anthony Ayers), 
       1943-|tPower sums, Gorenstein algebras, and determinantal 
       loci.|dBerlin ; New York : Springer, c1999|z3540667660
       |w(DLC)   99054164|w(OCoLC)42863051 
830  0 Lecture notes in mathematics (Springer-Verlag) ;|v1721 
856 40 |3SpringerLink|uhttp://www.springerlink.com/