Groups, generators, syzygies, and orbits in invariant theory

書誌事項

Groups, generators, syzygies, and orbits in invariant theory

V.L. Popov

(Translations of mathematical monographs, v. 100)

American Mathematical Society, c1992

  • : softcover

タイトル別名

Группы, образующие, сизигии и орбиты в теории инвариантов

Gruppy, obrazui︠u︡shchie, sizigii i orbity v teorii invariantov

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注記

Bibliographical references: p. 231-242

Includes index

内容説明・目次

内容説明

The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.

目次

Introduction Notation and terminology The role of reductive groups in invariant theory Constructive invariant theory The degree of the Poincare series of the algebra of invariants and a finiteness theorem for representations with free algebra of invariants Syzygies in invariant theory Representations with free modules of covariants A classification of normal affine quasihomogeneous varieties of SL2 Quasihomogeneous curves, surfaces, and solids Appendices Bibliography Subject index

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詳細情報

  • NII書誌ID(NCID)
    BA18250045
  • ISBN
    • 0821845578
    • 9780821853351
  • LCCN
    92010604
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 原本言語コード
    rus
  • 出版地
    Providence, R.I.
  • ページ数/冊数
    vi, 245 p.
  • 大きさ
    26 cm
  • 分類
  • 件名
  • 親書誌ID
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