Cohomology Of Quotients In Symplectic And Algebraic Geometry

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Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31

Author : Frances Clare Kirwan
Publisher : Princeton University Press
ISBN 13 : 0691214565
Total Pages : 216 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31 by : Frances Clare Kirwan

Download or read book Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31 written by Frances Clare Kirwan and published by Princeton University Press. This book was released on 2020-06-30 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These quotient varieties are interesting in particular because of their relevance to moduli problems in algebraic geometry. The author describes two different approaches to the problem. One is purely algebraic, while the other uses the methods of symplectic geometry and Morse theory, and involves extending classical Morse theory to certain degenerate functions.

The Cohomology of Quotients in Symplectic and Algebraic Geometry

Author : F. C. Kirwan
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (499 download)

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Book Synopsis The Cohomology of Quotients in Symplectic and Algebraic Geometry by : F. C. Kirwan

Download or read book The Cohomology of Quotients in Symplectic and Algebraic Geometry written by F. C. Kirwan and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hamiltonian Group Actions and Equivariant Cohomology

Author : Shubham Dwivedi
Publisher : Springer Nature
ISBN 13 : 3030272273
Total Pages : 132 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Hamiltonian Group Actions and Equivariant Cohomology by : Shubham Dwivedi

Download or read book Hamiltonian Group Actions and Equivariant Cohomology written by Shubham Dwivedi and published by Springer Nature. This book was released on 2019-09-23 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph could be used for a graduate course on symplectic geometry as well as for independent study. The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.

Lectures on Symplectic Geometry

Author : Ana Cannas da Silva
Publisher : Springer
ISBN 13 : 354045330X
Total Pages : 240 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva

Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Quantization of Singular Symplectic Quotients

Author : N.P. Landsman
Publisher : Birkhäuser
ISBN 13 : 3034883641
Total Pages : 360 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Quantization of Singular Symplectic Quotients by : N.P. Landsman

Download or read book Quantization of Singular Symplectic Quotients written by N.P. Landsman and published by Birkhäuser. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.

Cohomology of Quotients in Real Symplectic Geometry

Author : Nasser Heydari
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (132 download)

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Book Synopsis Cohomology of Quotients in Real Symplectic Geometry by : Nasser Heydari

Download or read book Cohomology of Quotients in Real Symplectic Geometry written by Nasser Heydari and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Author : A. Bialynicki-Birula
Publisher : Springer Science & Business Media
ISBN 13 : 3662050714
Total Pages : 248 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action by : A. Bialynicki-Birula

Download or read book Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action written by A. Bialynicki-Birula and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration

Author : Alfonso Zamora Saiz
Publisher : Springer Nature
ISBN 13 : 3030678296
Total Pages : 127 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration by : Alfonso Zamora Saiz

Download or read book Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration written by Alfonso Zamora Saiz and published by Springer Nature. This book was released on 2021-03-24 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.

Lectures on Invariant Theory

Author : Igor Dolgachev
Publisher : Cambridge University Press
ISBN 13 : 9780521525480
Total Pages : 244 pages
Book Rating : 4.5/5 (254 download)

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Book Synopsis Lectures on Invariant Theory by : Igor Dolgachev

Download or read book Lectures on Invariant Theory written by Igor Dolgachev and published by Cambridge University Press. This book was released on 2003-08-07 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Snowbird Lectures in Algebraic Geometry

Author : Ravi Vakil
Publisher : American Mathematical Soc.
ISBN 13 : 0821837192
Total Pages : 202 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Snowbird Lectures in Algebraic Geometry by : Ravi Vakil

Download or read book Snowbird Lectures in Algebraic Geometry written by Ravi Vakil and published by American Mathematical Soc.. This book was released on 2005 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate students and recent Ph.D.'s, to a wide swathe of algebraic geometry and giving them a working familiarity with exciting, rapidly developing parts of the field. One of the main goals of the organizers was to allow the participants to broaden their horizons beyond the narrow area in which they are working. A fine selection of topics and a noteworthy list of contributors made the resulting collection of articles a useful resource for everyone interested in getting acquainted with the modern topic of algebraic geometry. The book consists of ten articles covering, among others, the following topics: the minimal model program, derived categories of sheaves on algebraic varieties, Kobayashi hyperbolicity, groupoids and quotients in algebraic geometry, rigid analytic varieties, and equivariant cohomology. Suitable for independent study, this unique volume is intended for graduate students and researchers interested in algebraic geometry.

The Geometry of Cubic Hypersurfaces

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1009279998
Total Pages : 462 pages
Book Rating : 4.0/5 (92 download)

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Book Synopsis The Geometry of Cubic Hypersurfaces by : Daniel Huybrechts

Download or read book The Geometry of Cubic Hypersurfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2023-06-30 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.

Complex Geometry

Author : Daniel Huybrechts
Publisher : Springer Science & Business Media
ISBN 13 : 9783540212904
Total Pages : 336 pages
Book Rating : 4.2/5 (129 download)

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Book Synopsis Complex Geometry by : Daniel Huybrechts

Download or read book Complex Geometry written by Daniel Huybrechts and published by Springer Science & Business Media. This book was released on 2005 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)

Noncommutative Geometry and Cayley-smooth Orders

Author : Lieven Le Bruyn
Publisher : CRC Press
ISBN 13 : 1420064231
Total Pages : 592 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Noncommutative Geometry and Cayley-smooth Orders by : Lieven Le Bruyn

Download or read book Noncommutative Geometry and Cayley-smooth Orders written by Lieven Le Bruyn and published by CRC Press. This book was released on 2007-08-24 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry and Cayley-smooth Orders explains the theory of Cayley-smooth orders in central simple algebras over function fields of varieties. In particular, the book describes the etale local structure of such orders as well as their central singularities and finite dimensional representations. After an introduction to partial d

Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

Author : Jean H Gallier
Publisher : World Scientific
ISBN 13 : 9811245045
Total Pages : 799 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry by : Jean H Gallier

Download or read book Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry written by Jean H Gallier and published by World Scientific. This book was released on 2022-01-19 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.

ICM-90 Satellite Conference Proceedings

Author : Akira Fujiki
Publisher : Springer Science & Business Media
ISBN 13 : 4431681728
Total Pages : 265 pages
Book Rating : 4.4/5 (316 download)

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Book Synopsis ICM-90 Satellite Conference Proceedings by : Akira Fujiki

Download or read book ICM-90 Satellite Conference Proceedings written by Akira Fujiki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Conference "Algebraic Geometry and Analytic Geometry, Tokyo 1990" was held at Tokyo Metropolitan University and the Tokyo Training Center of Daihyaku Mutual Life Insurance Co., from August 13 through August 17, 1990, under the co-sponsorship of the Mathematical Society of Japan. It was one of the satellite conferences of ICM90, Kyoto, and approximately 300 participants, including more than 100 from overseas, attended the conference. The academic program was divided into two parts, the morning sessions and the afternoon sessions. The morning sessions were held at Tokyo Metropolitan University, and two one-hour plenary lectures were delivered every day. The afternoon sessions at the Tokyo Training Center, intended for a more specialized audience, consisted of four separate subsessions: Arithemetic Geometry, Algebraic Geometry, Analytic Geometry I and Analytic Geometry II. This book contains papers which grew out of the talks at the conference. The committee in charge of the organization and program consisted of A. Fujiki, K. Kato, T. Katsura, Y. Kawamata, Y. Miyaoka, S. Mori, K. Saito, N. Sasakura, T. Suwa and K. Watanabe. We would like to take this opportunity to thank the many mathematicians and students who cooperated to make the conference possible, especially Professors T. Fukui, S. Ishii, Y. Kitaoka, M. Miyanishi, Y. Namikawa, T. Oda, F. Sakai and T. Shioda for their valuable advice and assistance in organizing this conference. Financial support was mainly provided by personal contributions from Professors M.

A Celebration of the Mathematical Legacy of Raoul Bott

Author : Peter Robert Kotiuga
Publisher : American Mathematical Soc.
ISBN 13 : 082188381X
Total Pages : 418 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Celebration of the Mathematical Legacy of Raoul Bott by : Peter Robert Kotiuga

Download or read book A Celebration of the Mathematical Legacy of Raoul Bott written by Peter Robert Kotiuga and published by American Mathematical Soc.. This book was released on 2010-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in Topological Quantum Field Theory

Author : John M. Bryden
Publisher : Springer Science & Business Media
ISBN 13 : 1402027729
Total Pages : 353 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Advances in Topological Quantum Field Theory by : John M. Bryden

Download or read book Advances in Topological Quantum Field Theory written by John M. Bryden and published by Springer Science & Business Media. This book was released on 2007-09-27 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the conference proceedings of the NATO ARW during August 2001 at Kananaskis Village, Canada on 'New Techniques in Topological Quantum Field Theory'. This conference brought together specialists from a number of different fields all related to Topological Quantum Field Theory. The theme of this conference was to attempt to find new methods in quantum topology from the interaction with specialists in these other fields. The featured articles include papers by V. Vassiliev on combinatorial formulas for cohomology of spaces of Knots, the computation of Ohtsuki series by N. Jacoby and R. Lawrence, and a paper by M. Asaeda and J. Przytycki on the torsion conjecture for Khovanov homology by Shumakovitch. Moreover, there are articles on more classical topics related to manifolds and braid groups by such well known authors as D. Rolfsen, H. Zieschang and F. Cohen.