Algebraic Geometry IV

1. Front Matter

   Pages i-vii

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2. Linear Algebraic Groups

   • T. A. Springer

   Pages 1-121

3. Invariant Theory

   • V. L. Popov, E. B. Vinberg

   Pages 123-278

4. Back Matter

   Pages 279-286

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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.

• Algebra
• Invariant theory
• Invariantentheorie
• Quotientenvarietät
• Theoretical physics
• Wurzelsystem
• linear algebra
• linear algebraic groups
• lineare algebraische Gruppen
• quotient variety
• reductive group
• reduktive Gruppe
• root system

• Steklov Mathematical Institute, Moscow, Russia

  A. N. Parshin, I. R. Shafarevich

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