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Algebraic Geometry IV. Vol.4

  • Fester Einband
  • 286 Seiten
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Dieser EMS-Band, der Beiträge zu eng verwandten Gebieten enthält, wird als Nachschlagewerk und Führer zur aktuellen Forschung sehr... Weiterlesen
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Dieser EMS-Band, der Beiträge zu eng verwandten Gebieten enthält, wird als Nachschlagewerk und Führer zur aktuellen Forschung sehr nützlich sein. Springer ist ein bekannter Spezialist auf seinem Gebiet. Popov und Vinberg gehören zu den aktivsten Forschern in der Invariantentheorie.

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.

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.

I. Linear Algebraic Groups.- II. Invariant Theory.- Author Index.


Titel: Algebraic Geometry IV. Vol.4
Untertitel: Linear Algebraic Groups Invariant Theory
EAN: 9783540546825
ISBN: 978-3-540-54682-5
Format: Fester Einband
Herausgeber: Springer, Berlin
Genre: Mathematik
Anzahl Seiten: 286
Gewicht: 576g
Größe: H18mm x B243mm x T163mm
Jahr: 1994
Auflage: 1994. 1994

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