Lectures On Invariant Theory
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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.
Invariant Theory
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Author : T.A. Springer
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1977-05
Invariant Theory written by T.A. Springer and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-05 with Mathematics categories.
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.
Lectures On Invariant Theory
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Author : Igor Dolgachev
language : en
Publisher:
Release Date : 2003
Lectures On Invariant Theory written by Igor Dolgachev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Electronic books categories.
This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.
The Invariant Theory Of Matrices
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Author : Corrado De Concini
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-16
The Invariant Theory Of Matrices written by Corrado De Concini and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Mathematics categories.
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.
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory
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Author : Roger Howe
language : en
Publisher: World Scientific
Release Date : 2007
Harmonic Analysis Group Representations Automorphic Forms And Invariant Theory written by Roger Howe and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume carries the same title as that of an international conference held at the National University of Singapore, 9OCo11 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. Sample Chapter(s). Foreword (21 KB). Chapter 1: The Theta Correspondence Over R (342 KB). Contents: The Theta Correspondence over R (J Adams); The Heisenberg Group, SL (3, R), and Rigidity (A iap et al.); Pfaffians and Strategies for Integer Choice Games (R Evans & N Wallach); When is an L -Function Non-Vanishing in Part of the Critical Strip? (S Gelbart); Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L -Functions (M Harris); The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group (T Kobayashi & G Mano); Classification des S(r)ries Discr tes pour Certains Groupes Classiques p- Adiques (C Moeglin); Some Algebras of Essentially Compact Distributions of a Reductive p -Adic Group (A Moy & M Tadic); Annihilators of Generalized Verma Modules of the Scalar Type for Classical Lie Algebras (T Oshima); Branching to a Maximal Compact Subgroup (D A Vogan, Jr.); Small Semisimple Subalgebras of Semisimple Lie Algebras (J F Willenbring & G J Zuckerman). Readership: Graduate students and research mathematicians in harmonic analysis, group representations, automorphic forms and invariant theory."
The Theory Of Algebraic Number Fields
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Author : David Hilbert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Theory Of Algebraic Number Fields written by David Hilbert 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 2013-03-14 with Mathematics categories.
Constance Reid, in Chapter VII of her book Hilbert, tells the story of the writing of the Zahlbericht, as his report entitled Die Theorie der algebra is chen Zahlkorper has always been known. At its annual meeting in 1893 the Deutsche Mathematiker-Vereinigung (the German Mathematical Society) invited Hilbert and Minkowski to prepare a report on the current state of affairs in the theory of numbers, to be completed in two years. The two mathematicians agreed that Minkowski should write about rational number theory and Hilbert about algebraic number theory. Although Hilbert had almost completed his share of the report by the beginning of 1896 Minkowski had made much less progress and it was agreed that he should withdraw from his part of the project. Shortly afterwards Hilbert finished writing his report on algebraic number fields and the manuscript, carefully copied by his wife, was sent to the printers. The proofs were read by Minkowski, aided in part by Hurwitz, slowly and carefully, with close attention to the mathematical exposition as well as to the type-setting; at Minkowski's insistence Hilbert included a note of thanks to his wife. As Constance Reid writes, "The report on algebraic number fields exceeded in every way the expectation of the members of the Mathemati cal Society. They had asked for a summary of the current state of affairs in the theory. They received a masterpiece, which simply and clearly fitted all the difficult developments of recent times into an elegantly integrated theory.
Invariant Manifolds
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Author : M.W. Hirsch
language : en
Publisher: Springer
Release Date : 2006-11-15
Invariant Manifolds written by M.W. Hirsch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Algebraic Cycles And Hodge Theory
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Author : Mark L. Green
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-12-16
Algebraic Cycles And Hodge Theory written by Mark L. Green 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 1994-12-16 with Mathematics categories.
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.