The 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.

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:

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.

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.

Geometry and Quantum Field Theory

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
ISBN 13 : 9780821886830
Total Pages : 476 pages
Book Rating : 4.8/5 (868 download)

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Book Synopsis Geometry and Quantum Field Theory by : Daniel S. Freed

Download or read book Geometry and Quantum Field Theory written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 1995 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.

Mod Two Homology and Cohomology

Author : Jean-Claude Hausmann
Publisher : Springer
ISBN 13 : 3319093541
Total Pages : 539 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Mod Two Homology and Cohomology by : Jean-Claude Hausmann

Download or read book Mod Two Homology and Cohomology written by Jean-Claude Hausmann and published by Springer. This book was released on 2015-01-08 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology and homology modulo 2 helps the reader grasp more readily the basics of a major tool in algebraic topology. Compared to a more general approach to (co)homology this refreshing approach has many pedagogical advantages: 1. It leads more quickly to the essentials of the subject, 2. An absence of signs and orientation considerations simplifies the theory, 3. Computations and advanced applications can be presented at an earlier stage, 4. Simple geometrical interpretations of (co)chains. Mod 2 (co)homology was developed in the first quarter of the twentieth century as an alternative to integral homology, before both became particular cases of (co)homology with arbitrary coefficients. The first chapters of this book may serve as a basis for a graduate-level introductory course to (co)homology. Simplicial and singular mod 2 (co)homology are introduced, with their products and Steenrod squares, as well as equivariant cohomology. Classical applications include Brouwer's fixed point theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith theory, Kervaire invariant, etc. The cohomology of flag manifolds is treated in detail (without spectral sequences), including the relationship between Stiefel-Whitney classes and Schubert calculus. More recent developments are also covered, including topological complexity, face spaces, equivariant Morse theory, conjugation spaces, polygon spaces, amongst others. Each chapter ends with exercises, with some hints and answers at the end of the book.

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.

Poisson Geometry in Mathematics and Physics

Author : Giuseppe Dito
Publisher : American Mathematical Soc.
ISBN 13 : 0821844237
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Poisson Geometry in Mathematics and Physics by : Giuseppe Dito

Download or read book Poisson Geometry in Mathematics and Physics written by Giuseppe Dito and published by American Mathematical Soc.. This book was released on 2008 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of articles by speakers at the Poisson 2006 conference. The program for Poisson 2006 was an overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction.

Interactions with Lattice Polytopes

Author : Alexander M. Kasprzyk
Publisher : Springer Nature
ISBN 13 : 3030983277
Total Pages : 368 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Interactions with Lattice Polytopes by : Alexander M. Kasprzyk

Download or read book Interactions with Lattice Polytopes written by Alexander M. Kasprzyk and published by Springer Nature. This book was released on 2022-06-08 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics. Covering a diverse range of topics, including algebraic geometry, mirror symmetry, symplectic geometry, discrete geometry, and algebraic combinatorics, the common theme is the study of lattice polytopes. These fascinating combinatorial objects are a cornerstone of toric geometry and continue to find rich and unforeseen applications throughout mathematics. The workshop Interactions with Lattice Polytopes assembled many top researchers at the Otto-von-Guericke-Universität Magdeburg in 2017 to discuss the role of lattice polytopes in their work, and many of their presented results are collected in this book. Intended to be accessible, these articles are suitable for researchers and graduate students interested in learning about some of the wide-ranging interactions of lattice polytopes in pure mathematics.

Mirror Symmetry IV

Author : Eric D'Hoker
Publisher : American Mathematical Soc.
ISBN 13 : 0821833359
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mirror Symmetry IV by : Eric D'Hoker

Download or read book Mirror Symmetry IV written by Eric D'Hoker and published by American Mathematical Soc.. This book was released on 2002 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions of participants of a workshop held at the Centre de Recherches Mathematiques (CRM), University of Montreal. It can be viewed as a sequel to Mirror Symmetry I (1998), Mirror Symmetry II (1996), and Mirror Symmetry III (1999), copublished by the AMS and International Press. The volume presents a broad survey of many of the noteworthy developments that have taken place in string theory, geometry, and duality since the mid 1990s. Some of the topics emphasized include the following: Integrable models and supersymmetric gauge theories; theory of M- and D-branes and noncommutative geometry; duality between strings and gauge theories; and elliptic genera and automorphic forms. Several introductory articles present an overview of the geometric and physical aspects of mirror symmetry and of corresponding developments in symplectic geometry. The book provides an efficient way for a very broad audience of mathematicians and physicists to explore the frontiers of research into this rapidly expanding area.

Special Metrics and Group Actions in Geometry

Author : Simon G. Chiossi
Publisher : Springer
ISBN 13 : 3319675192
Total Pages : 338 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Special Metrics and Group Actions in Geometry by : Simon G. Chiossi

Download or read book Special Metrics and Group Actions in Geometry written by Simon G. Chiossi and published by Springer. This book was released on 2017-11-27 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

Vector Bundles in Algebraic Geometry

Author : N. J. Hitchin
Publisher : Cambridge University Press
ISBN 13 : 0521498783
Total Pages : 359 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Vector Bundles in Algebraic Geometry by : N. J. Hitchin

Download or read book Vector Bundles in Algebraic Geometry written by N. J. Hitchin and published by Cambridge University Press. This book was released on 1995-03-16 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of survey articles by the main speakers at the 1993 Durham symposium on vector bundles in algebraic geometry.

Lectures on Hilbert Schemes of Points on Surfaces

Author : Hiraku Nakajima
Publisher : American Mathematical Soc.
ISBN 13 : 0821819569
Total Pages : 146 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lectures on Hilbert Schemes of Points on Surfaces by : Hiraku Nakajima

Download or read book Lectures on Hilbert Schemes of Points on Surfaces written by Hiraku Nakajima and published by American Mathematical Soc.. This book was released on 1999 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.

Moduli Spaces and Vector Bundles—New Trends

Author : Peter Gothen
Publisher : American Mathematical Society
ISBN 13 : 1470472961
Total Pages : 382 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Moduli Spaces and Vector Bundles—New Trends by : Peter Gothen

Download or read book Moduli Spaces and Vector Bundles—New Trends written by Peter Gothen and published by American Mathematical Society. This book was released on 2024-07-18 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the VBAC 2022 Conference on Moduli Spaces and Vector Bundles—New Trends, held in honor of Peter Newstead's 80th birthday, from July 25–29, 2022, at the University of Warwick, Coventry, United Kingdom. The papers focus on the theory of stability conditions in derived categories, non-reductive geometric invariant theory, Brill-Noether theory, and Higgs bundles and character varieties. The volume includes both survey and original research articles. Most articles contain substantial background and will be helpful to both novices and experts.