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

Author: A. Bialynicki-Birula
Publisher: Springer Science & Business Media
ISBN: 9783540432111
Size: 46.69 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
Publisher: CRC Press
ISBN: 1351644777
Size: 39.67 MB
Format: PDF
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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
Publisher: Springer Science & Business Media
ISBN: 9783764385378
Size: 54.35 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.

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

Author: A. Bialynicki-Birula
Publisher: Springer Science & Business Media
ISBN: 3662050714
Size: 51.69 MB
Format: PDF, ePub, Docs
View: 2594
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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
Publisher:
ISBN:
Size: 41.91 MB
Format: PDF, Kindle
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Algebraic Theory Of Locally Nilpotent Derivations

Author: Gene Freudenburg
Publisher: Springer
ISBN: 3662553503
Size: 25.49 MB
Format: PDF
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This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves. More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem. A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.

Linear Algebraic Monoids

Author: Lex Renner
Publisher: Springer Science & Business Media
ISBN: 3540275568
Size: 77.21 MB
Format: PDF, Mobi
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This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.

The Geometry Of Infinite Dimensional Groups

Author: Boris Khesin
Publisher: Springer Science & Business Media
ISBN: 3540772634
Size: 34.69 MB
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This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.

Cox Rings

Author: Ivan Arzhantsev
Publisher: Cambridge University Press
ISBN: 1316147959
Size: 20.94 MB
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Cox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces. This book provides a largely self-contained introduction to Cox rings, with a particular focus on concrete aspects of the theory. Besides the rigorous presentation of the basic concepts, other central topics include the case of finitely generated Cox rings and its relation to toric geometry; various classes of varieties with group actions; the surface case; and applications in arithmetic problems, in particular Manin's conjecture. The introductory chapters require only basic knowledge in algebraic geometry. The more advanced chapters also touch on algebraic groups, surface theory, and arithmetic geometry. Each chapter ends with exercises and problems. These comprise mini-tutorials and examples complementing the text, guided exercises for topics not discussed in the text, and, finally, several open problems of varying difficulty.