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Geometric Invariant Theory


Geometric Invariant Theory
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Lectures On Invariant Theory


Lectures On Invariant Theory
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Author : Igor Dolgachev
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-07

Lectures On Invariant Theory written by Igor Dolgachev and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-07 with Mathematics categories.


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.



Geometric Invariant Theory And Decorated Principal Bundles


Geometric Invariant Theory And Decorated Principal Bundles
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Author : Alexander H. W. Schmitt
language : en
Publisher: European Mathematical Society
Release Date : 2008

Geometric Invariant Theory And Decorated Principal Bundles written by Alexander H. W. Schmitt and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.


The book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness of the number of quotients, and the variation of quotients. In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map. Via the universal Kobayashi-Hitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces. The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles. The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry.



Computational Invariant Theory


Computational Invariant Theory
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Author : Harm Derksen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Computational Invariant Theory written by Harm Derksen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.


Invariant theory is a subject with a long tradition and an astounding abil ity to rejuvenate itself whenever it reappears on the mathematical stage. Throughout the history of invariant theory, two features of it have always been at the center of attention: computation and applications. This book is about the computational aspects of invariant theory. We present algorithms for calculating the invariant ring of a group that is linearly reductive or fi nite, including the modular case. These algorithms form the central pillars around which the book is built. To prepare the ground for the algorithms, we present Grabner basis methods and some general theory of invariants. Moreover, the algorithms and their behavior depend heavily on structural properties of the invariant ring to be computed. Large parts of the book are devoted to studying such properties. Finally, most of the applications of in variant theory depend on the ability to calculate invariant rings. The last chapter of this book provides a sample of applications inside and outside of mathematics.



Introduction To Geometric Invariant Theory


Introduction To Geometric Invariant Theory
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Author : Igor V. Dolgachev
language : en
Publisher:
Release Date : 1994

Introduction To Geometric Invariant Theory written by Igor V. Dolgachev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Geometry, Algebraic categories.




Classical Invariant Theory


Classical Invariant Theory
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Author : Peter J. Olver
language : en
Publisher: Cambridge University Press
Release Date : 1999-01-13

Classical Invariant Theory written by Peter J. Olver and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-13 with Mathematics categories.


The book is a self-contained introduction to the results and methods in classical invariant theory.



Algebraic Geometry Iv


Algebraic Geometry Iv
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Author : A.N. Parshin
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-04-25

Algebraic Geometry Iv written by A.N. Parshin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-25 with Mathematics categories.


Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.



Geometric Invariant Theory


Geometric Invariant Theory
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Author : David Mumford
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-03-29

Geometric Invariant Theory written by David Mumford and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-03-29 with Mathematics categories.


This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.



Algorithms In Invariant Theory


Algorithms In Invariant Theory
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Author : Bernd Sturmfels
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-17

Algorithms In Invariant Theory written by Bernd Sturmfels and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-17 with Mathematics categories.


This book is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to research ideas, hints for applications, outlines and details of algorithms, examples and problems.



Introduction To Moduli Problems And Orbit Spaces


Introduction To Moduli Problems And Orbit Spaces
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Author : P. E. Newstead
language : en
Publisher: Alpha Science International Limited
Release Date : 2012

Introduction To Moduli Problems And Orbit Spaces written by P. E. Newstead and has been published by Alpha Science International Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.


Geometric Invariant Theory (GIT), developed in the 1960s by David Mumford, is the theory of quotients by group actions in Algebraic Geometry. Its principal application is to the construction of various moduli spaces. Peter Newstead gave a series of lectures in 1975 at the Tata Institute of Fundamental Research, Mumbai on GIT and its application to the moduli of vector bundles on curves. It was a masterful yet easy to follow exposition of important material, with clear proofs and many examples. The notes, published as a volume in the TIFR lecture notes series, became a classic, and generations of algebraic geometers working in these subjects got their basic introduction to this area through these lecture notes. Though continuously in demand, these lecture notes have been out of print for many years. The Tata Institute is happy to re-issue these notes in a new print.



Differential Geometry In The Large


Differential Geometry In The Large
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Author : Owen Dearricott
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-22

Differential Geometry In The Large written by Owen Dearricott and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Mathematics categories.


From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.