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Standard Monomial Theory

  • Fester Einband
  • 266 Seiten
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Leseprobe
Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation theory. Th... Weiterlesen
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Beschreibung

Schubert varieties lie at the cross roads of algebraic geometry, combinatorics, commutative algebra, and representation theory. They are an important class of subvarieties of flag varieties, interesting in their own right, and providing an inductive tool for studying flag varieties. The literature on them is vast, for they are ubiquitousthey have been intensively studied over the last fifty years, from many different points of view and by many different authors.

This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory on the one hand and standard monomial theory for Schubert varieties in certain special flag varieties - the ordinary, orthogonal, and symplectic Grassmannians - on the other. Historically, this connection was the prime motivation for the development of standard monomial theory. Determinantal varieties and basic concepts of geometric invariant theory arise naturally in establishing the connection.

The book also treats, in the last chapter, some other applications of standard monomial theory, e.g., to the study of certain naturally occurring affine algebraic varieties that, like determinantal varieties, can be realized as open parts of Schubert varieties.



Excellent overview of the theory of Schubert varieties



Inhalt
Generalities on algebraic varieties.- Generalities on algebraic groups.- Grassmannian.- Determinantal varieties.- Symplectic Grassmannian.- Orthogonal Grassmannian.- The standard monomial theoretic basis.- Review of GIT.- Invariant theory.- SLn(K)-action.- SOn(K)-action.- Applications of standard monomial theory.

Produktinformationen

Titel: Standard Monomial Theory
Untertitel: Invariant Theoretic Approach
Autor:
EAN: 9783540767565
ISBN: 3540767568
Format: Fester Einband
Herausgeber: Springer-Verlag GmbH
Anzahl Seiten: 266
Gewicht: 588g
Größe: H241mm x B160mm x T20mm
Jahr: 2008
Auflage: 2008

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