Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action
Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action

Author: A. Bialynicki-Birula

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 248

ISBN-13: 3662050714

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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
Actions and Invariants of Algebraic Groups

Author: Walter Ricardo Ferrer Santos

Publisher: CRC Press

Published: 2017-09-19

Total Pages: 709

ISBN-13: 1351644777

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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.

Facets of Algebraic Geometry
Facets of Algebraic Geometry

Author: Paolo Aluffi

Publisher: Cambridge University Press

Published: 2022-04-07

Total Pages: 395

ISBN-13: 1108792510

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Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.

Cox Rings
Cox Rings

Author: Ivan Arzhantsev

Publisher: Cambridge University Press

Published: 2015

Total Pages: 539

ISBN-13: 1107024625

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This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.

Actions and Invariants of Algebraic Groups
Actions and Invariants of Algebraic Groups

Author: Walter Ferrer Santos

Publisher: CRC Press

Published: 2005-04-26

Total Pages: 472

ISBN-13: 1420030795

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Actions and Invariants of Algebraic Groups presents a self-contained introduction to geometric invariant theory that links the basic theory of affine algebraic groups to Mumford's more sophisticated theory. The authors systematically exploit the viewpoint of Hopf algebra theory and the theory of comodules to simplify and compactify many of the rele

Algebraic Cycles, Sheaves, Shtukas, and Moduli
Algebraic Cycles, Sheaves, Shtukas, and Moduli

Author: Piotr Pragacz

Publisher: Springer Science & Business Media

Published: 2008-03-12

Total Pages: 240

ISBN-13: 3764385375

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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.

Proceedings of the International Colloquium on Algebraic Groups and Homogeneous Spaces
Proceedings of the International Colloquium on Algebraic Groups and Homogeneous Spaces

Author: V. B. Mehta

Publisher: Alpha Science International, Limited

Published: 2007

Total Pages: 564

ISBN-13:

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The area of algebraic groups and homogeneous spaces is one in which major advances have been made in recent decades. This was the theme of the (twelfth) International Colloquium organized by the Tata Institute of Fundamental Research in January 2004, and this volume constitutes the proceedings of that meeting. This volume contains articles by several leading experts in central topics in the area, including representation theory, flag varieties, Schubert varieties, vector bundles, loop groups and Kac-Moody Lie algebras, Galois cohomology of algebraic groups, and Tannakian categories. In addition to the original papers in these areas, the volume includes a survey on representation theory in characteristic $p$ by H. Andersen and an article by T. A. Springer on Armand Borel's work in algebraic groups and Lie groups.

Representations of Algebraic Groups
Representations of Algebraic Groups

Author: Jens Carsten Jantzen

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 594

ISBN-13: 082184377X

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Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.