Lectures On Invariant Theory

Author : Igor Dolgachev
Publisher : Cambridge University Press
Page : 244 pages
File Size : 54,6 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0521525489

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Lectures on Invariant Theory by Igor Dolgachev Pdf

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.

Author : T.A. Springer
Publisher : Springer
Page : 118 pages
File Size : 43,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540373704

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Invariant Theory by T.A. Springer Pdf

Author : Alexander H. W. Schmitt
Publisher : European Mathematical Society
Page : 404 pages
File Size : 42,8 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190655

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Geometric Invariant Theory and Decorated Principal Bundles by Alexander H. W. Schmitt Pdf

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.

Author : Igor V. Dolgachev
Publisher : Unknown
Page : 237 pages
File Size : 52,7 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362261

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Lectures on Invariant Theory by Igor V. Dolgachev Pdf

This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.

Author : Shigeru Mukai
Publisher : Cambridge University Press
Page : 528 pages
File Size : 54,9 Mb
Release : 2003-09-08
Category : Mathematics
ISBN : 0521809061

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An Introduction to Invariants and Moduli by Shigeru Mukai Pdf

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Author : Corrado De Concini,Claudio Procesi
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 42,7 Mb
Release : 2017-11-16
Category : Invariants
ISBN : 9781470441876

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The Invariant Theory of Matrices by Corrado De Concini,Claudio Procesi Pdf

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.

Author : David Hilbert
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 49,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662035450

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The Theory of Algebraic Number Fields by David Hilbert Pdf

A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.

Author : Marcos Marino,Michael Thaddeus,Ravi Vakil
Publisher : Springer
Page : 210 pages
File Size : 54,8 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9783540798149

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Enumerative Invariants in Algebraic Geometry and String Theory by Marcos Marino,Michael Thaddeus,Ravi Vakil Pdf

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.

Author : Jian-Shu Li
Publisher : World Scientific
Page : 446 pages
File Size : 43,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770783

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Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory by Jian-Shu Li Pdf

This volume carries the same title as that of an international conference held at the National University of Singapore, 9-11 January 2006 on the occasion of Roger E. Howe's 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe's mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications.

Author : Peter J. Olver
Publisher : Cambridge University Press
Page : 308 pages
File Size : 46,6 Mb
Release : 1999-01-13
Category : Mathematics
ISBN : 0521558212

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Classical Invariant Theory by Peter J. Olver Pdf

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

Author : John Fogarty
Publisher : Unknown
Page : 240 pages
File Size : 43,9 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39015049069365

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Invariant Theory by John Fogarty Pdf

Author : Mark Pollicott
Publisher : Cambridge University Press
Page : 176 pages
File Size : 49,8 Mb
Release : 1993-02-04
Category : Mathematics
ISBN : 0521435935

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Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds by Mark Pollicott Pdf

These lecture notes provide a unique introduction to Pesin theory and its applications.

Author : Roe Goodman,Nolan R. Wallach
Publisher : Springer Science & Business Media
Page : 731 pages
File Size : 44,6 Mb
Release : 2009-07-30
Category : Mathematics
ISBN : 9780387798523

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Symmetry, Representations, and Invariants by Roe Goodman,Nolan R. Wallach Pdf

Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.

Author : P. E. Newstead
Publisher : Alpha Science International Limited
Page : 166 pages
File Size : 41,6 Mb
Release : 2012
Category : Mathematics
ISBN : 8184871627

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Introduction to Moduli Problems and Orbit Spaces by P. E. Newstead Pdf

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.

Author : John D. Moore
Publisher : Springer
Page : 113 pages
File Size : 52,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540685920

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Lectures on Seiberg-Witten Invariants by John D. Moore Pdf

In the fall of 1994, Edward Witten proposed a set of equations which give the main results of Donaldson theory in a far simpler way than had been thought possible. The purpose of these notes is to provide an elementary introduction to the equations that Witten proposed. They are directed towards graduate students who have already taken a basic course in differential geometry and topology.