Geometric Invariant Theory

Geometric Invariant Theory PDF
Author: David Mumford
Publisher: Springer Science & Business Media
ISBN: 9783540569633
Size: 64.11 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 292
View: 3381

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Geometric Invariant Theory

by David Mumford, Geometric Invariant Theory Books available in PDF, EPUB, Mobi Format. Download Geometric Invariant Theory books, "Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants.


Geometric Invariant Theory

Geometric Invariant Theory PDF
Author: David Mumford
Publisher: Springer
ISBN:
Size: 48.29 MB
Format: PDF, Docs
Category : Geometry, Algebraic
Languages : en
Pages : 219
View: 5586

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Geometric Invariant Theory

by David Mumford, Geometric Invariant Theory Books available in PDF, EPUB, Mobi Format. Download Geometric Invariant Theory books, 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.


Geometric Invariant Theory

Geometric Invariant Theory PDF
Author: David Mumford
Publisher:
ISBN:
Size: 45.20 MB
Format: PDF, ePub, Mobi
Category : Geometry, Algebraic
Languages : en
Pages : 145
View: 1278

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Geometric Invariant Theory

by David Mumford, Geometric Invariant Theory Books available in PDF, EPUB, Mobi Format. Download Geometric Invariant Theory books, 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.


Geometric Invariant Theory

Geometric Invariant Theory PDF
Author: Nolan R. Wallach
Publisher: Springer
ISBN: 3319659073
Size: 33.52 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 190
View: 2603

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Geometric Invariant Theory

by Nolan R. Wallach, Geometric Invariant Theory Books available in PDF, EPUB, Mobi Format. Download Geometric Invariant Theory books, Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry. Throughout the book, examples are emphasized. Exercises add to the reader’s understanding of the material; most are enhanced with hints. The exposition is divided into two parts. The first part, ‘Background Theory’, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic groups. Part 2, ‘Geometric Invariant Theory’ consists of three chapters (3–5). Chapter 3 centers on the Hilbert–Mumford theorem and contains a complete development of the Kempf–Ness theorem and Vindberg’s theory. Chapter 4 studies the orbit structure of a reductive algebraic group on a projective variety emphasizing Kostant’s theory. The final chapter studies the extension of classical invariant theory to products of classical groups emphasizing recent applications of the theory to physics.


Geometric Invariant Theory And Decorated Principal Bundles

Geometric Invariant Theory and Decorated Principal Bundles PDF
Author: Alexander H. W. Schmitt
Publisher: European Mathematical Society
ISBN: 9783037190654
Size: 42.41 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 389
View: 1862

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Geometric Invariant Theory And Decorated Principal Bundles

by Alexander H. W. Schmitt, Geometric Invariant Theory And Decorated Principal Bundles Books available in PDF, EPUB, Mobi Format. Download Geometric Invariant Theory And Decorated Principal Bundles books, 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.


Lectures On Invariant Theory

Lectures on Invariant Theory PDF
Author: Igor Dolgachev
Publisher: Cambridge University Press
ISBN: 9780521525480
Size: 17.96 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 220
View: 5951

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Lectures On Invariant Theory

by Igor Dolgachev, Lectures On Invariant Theory Books available in PDF, EPUB, Mobi Format. Download Lectures On Invariant Theory books, 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 For Polarized Curves

Geometric Invariant Theory for Polarized Curves PDF
Author: Gilberto Bini
Publisher: Springer
ISBN: 3319113372
Size: 27.55 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 211
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Geometric Invariant Theory For Polarized Curves

by Gilberto Bini, Geometric Invariant Theory For Polarized Curves Books available in PDF, EPUB, Mobi Format. Download Geometric Invariant Theory For Polarized Curves books, We investigate GIT quotients of polarized curves. More specifically, we study the GIT problem for the Hilbert and Chow schemes of curves of degree d and genus g in a projective space of dimension d-g, as d decreases with respect to g. We prove that the first three values of d at which the GIT quotients change are given by d=a(2g-2) where a=2, 3.5, 4. We show that, for a>4, L. Caporaso's results hold true for both Hilbert and Chow semistability. If 3.5a


Invariant Theory

Invariant Theory PDF
Author: R. Fossum
Publisher: American Mathematical Soc.
ISBN: 0821850946
Size: 29.17 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 598
View: 4836

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Invariant Theory

by R. Fossum, Invariant Theory Books available in PDF, EPUB, Mobi Format. Download Invariant Theory books,