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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.
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Table of contents (2 chapters)
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Front Matter
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Back Matter
Editors and Affiliations
Bibliographic Information
Book Title: Algebraic Geometry IV
Book Subtitle: Linear Algebraic Groups Invariant Theory
Editors: A. N. Parshin, I. R. Shafarevich
Series Title: Encyclopaedia of Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-662-03073-8
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1994
Hardcover ISBN: 978-3-540-54682-5Published: 25 April 1994
Softcover ISBN: 978-3-642-08119-4Published: 01 December 2010
eBook ISBN: 978-3-662-03073-8Published: 06 December 2012
Series ISSN: 0938-0396
Edition Number: 1
Number of Pages: X, 286
Additional Information: Original Russian edition published by VINITI, Moscow 1989
Topics: Algebraic Geometry, Topological Groups, Lie Groups, Algebra, Theoretical, Mathematical and Computational Physics