Lectures on invariant theory

Igor Dolgachev

236 pages, parution le 01/08/2003

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Résumé

The primary goal of this book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry.

Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Introduction

The symbolic method
The first fundamental theorem
Reductive algebraic groups
Hilbert's fourteenth problem
Algebra of covariants
Quotients
Linearization of actions
Stability
Numerical criterion of stability
Projective hypersurfaces
Configurations of linear subspaces
Toric varieties

Bibliography
Index of notation
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Igor Dolgachev
Parution	01/08/2003
Nb. de pages	236
Format	15 x 22,7
Couverture	Broché
Poids	320g
Intérieur	Noir et Blanc
EAN13	9780521525480
ISBN13	978-0-521-52548-0