algebraic quotients torus actions and cohomology the adjoint representation and the adjoint action encyclopaedia of mathematical sciences

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Algebraic Quotients Torus Actions And Cohomology The Adjoint Representation And The Adjoint Action

Author : A. Bialynicki-Birula
ISBN : 3540432116
Genre : Mathematics
File Size : 78. 72 MB
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This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.

Actions And Invariants Of Algebraic Groups Second Edition

Author : Walter Ricardo Ferrer Santos
ISBN : 9781351644778
Genre : Mathematics
File Size : 75. 15 MB
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Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.

Algebraic Cycles Sheaves Shtukas And Moduli

Author : Piotr Pragacz
ISBN : 3764385375
Genre : Mathematics
File Size : 80. 33 MB
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Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.

Mathematical Reviews

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ISBN : UVA:X006180437
Genre : Mathematics
File Size : 53. 40 MB
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Algebraic Quotients Torus Actions And Cohomology The Adjoint Representation And The Adjoint Action

Author : A. Bialynicki-Birula
ISBN : 9783662050712
Genre : Mathematics
File Size : 32. 65 MB
Format : PDF
Download : 143
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This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.

Newsletter

Author : New Zealand Mathematical Society
ISBN : UOM:39015057376611
Genre : Mathematics
File Size : 71. 82 MB
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Several Complex Variables Iii

Author : G.M. Khenkin
ISBN : 9783642613081
Genre : Mathematics
File Size : 23. 67 MB
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We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space

Algebraic Theory Of Locally Nilpotent Derivations

Author : Gene Freudenburg
ISBN : 9783540295235
Genre : Mathematics
File Size : 88. 41 MB
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This book explores the theory and application of locally nilpotent derivations. It provides a unified treatment of the subject, beginning with sixteen First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler’s Theorem for the plane, right up to the most recent results, such as Makar-Limanov’s Theorem for locally nilpotent derivations of polynomial rings. The book also includes a wealth of pexamples and open problems.

Standard Monomial Theory

Author : V. Lakshmibai
ISBN : 3540767576
Genre : Mathematics
File Size : 85. 66 MB
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Schubert varieties provide an inductive tool for studying flag varieties. This book is mainly a detailed account of a particularly interesting instance of their occurrence: namely, in relation to classical invariant theory. More precisely, it is about the connection between the first and second fundamental theorems of classical invariant theory on the one hand and standard monomial theory for Schubert varieties in certain special flag varieties on the other.

Lie Groups And Geometric Aspects Of Isometric Actions

Author : Marcos M. Alexandrino
ISBN : 9783319166131
Genre : Mathematics
File Size : 79. 69 MB
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This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.

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