Algebraic Geometry IV: Linear Algebraic Groups Invariant Theory (Encyclopaedia of Mathematical Sciences, 55)

Popov, V.L., Springer, T.A., Vinberg, E.B., Parshin, A.N., Shafarevich, I.R.

ISBN 10: 3540546820 / ISBN 13: 9783540546825

Published by Springer, 1994

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Bibliographic Details

Title: Algebraic Geometry IV: Linear Algebraic ...

Publisher: Springer

Publication Date: 1994

Binding: Hardcover

Condition: Fine

About this title

Synopsis:

The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the "reduction to canonical form" of various is almost the same thing, projective geometry. objects of linear algebra or, what Invariant theory has a ISO-year history, which has seen alternating periods of growth and stagnation, and changes in the formulation of problems, methods of solution, and fields of application. In the last two decades invariant theory has experienced a period of growth, stimulated by a previous development of the theory of algebraic groups and commutative algebra. It is now viewed as a branch of the theory of algebraic transformation groups (and under a broader interpretation can be identified with this theory). We will freely use the theory of algebraic groups, an exposition of which can be found, for example, in the first article of the present volume. We will also assume the reader is familiar with the basic concepts and simplest theorems of commutative algebra and algebraic geometry; when deeper results are needed, we will cite them in the text or provide suitable references.