Algebraic Geometry IV : Linear Algebraic Groups Invariant Theory

A. N. Parshin

ISBN 10: 3642081193 / ISBN 13: 9783642081194

Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg, 2010

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783642081194

Dati bibliografici

• Titolo: Algebraic Geometry IV : Linear Algebraic Groups Invariant Theory
• Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 3642081193
• ISBN 13: 9783642081194
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 234 L x 156 A x 17 P (millimetri) 234 millimetri di larghezza per 156 millimetri di altezza per 17 millimetri di profondità
• Peso: 453 grammi

Descrizione articolo

Riassunto

This volume of the Encyclopaedia contains two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory. The first part is written by T.A. Springer, a well-known expert in the first mentioned field. He presents a comprehensive survey, which contains numerous sketched proofs and he discusses the particular features of algebraic groups over special fields (finite, local, and global). The authors of Part II - E.B.Vinberg and V.L.Popov - are among the most active researchers in invariant theory. The last 20 years have been a period of vigorous development in this field due to the influence of modern methods from algebraic geometry. This book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.

Reseña del editor

Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.