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140122  eng 
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a 9783540467076

100 
1 

a Iarrobino, Anthony

245 
0 
0 
a Power Sums, Gorenstein Algebras, and Determinantal Loci
h Elektronische Ressource
c by Anthony Iarrobino, Vassil Kanev

250 


a 1st ed. 1999

260 


a Berlin, Heidelberg
b Springer Berlin Heidelberg
c 1999, 1999

300 


a XXXIV, 354 p
b online resource

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 zerodimensional schemes I: Basic results, and the case r=3  Forms and zerodimensional 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

653 


a Associative algebras

653 


a Algebraic Geometry

653 


a Associative rings

653 


a Algebraic geometry

653 


a Associative Rings and Algebras

700 
1 

a Kanev, Vassil
e [author]

041 
0 
7 
a eng
2 ISO 6392

989 


b SBA
a Springer Book Archives 2004

490 
0 

a Lecture Notes in Mathematics

028 
5 
0 
a 10.1007/BFb0093426

856 
4 
0 
u https://doi.org/10.1007/BFb0093426?nosfx=y
x Verlag
3 Volltext

082 
0 

a 516.35

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 GorensteinArtin algebras, and of Hilbert schemes of zerodimensional 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
