Lectures On Invariant Theory

Author : Igor Dolgachev
Publisher : Cambridge University Press
ISBN 13 : 9780521525480
Total Pages : 244 pages
Book Rating : 4.89/5 ( download)

DOWNLOAD NOW!

Download or read book Lectures on Invariant Theory written by Igor Dolgachev and published by Cambridge University Press. This book was released on 2003-08-07 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 3540373705
Total Pages : 118 pages
Book Rating : 4.04/5 ( download)

DOWNLOAD NOW!

Download or read book Invariant Theory written by T.A. Springer and published by Springer. This book was released on 2006-11-14 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alexander H. W. Schmitt
Publisher : European Mathematical Society
ISBN 13 : 9783037190654
Total Pages : 404 pages
Book Rating : 4.55/5 ( download)

DOWNLOAD NOW!

Download or read book Geometric Invariant Theory and Decorated Principal Bundles written by Alexander H. W. Schmitt and published by European Mathematical Society. This book was released on 2008 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : David Hilbert
Publisher : Springer Science & Business Media
ISBN 13 : 3662035456
Total Pages : 360 pages
Book Rating : 4.50/5 ( download)

DOWNLOAD NOW!

Download or read book The Theory of Algebraic Number Fields written by David Hilbert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Shigeru Mukai
Publisher : Cambridge University Press
ISBN 13 : 9780521809061
Total Pages : 528 pages
Book Rating : 4.61/5 ( download)

DOWNLOAD NOW!

Download or read book An Introduction to Invariants and Moduli written by Shigeru Mukai and published by Cambridge University Press. This book was released on 2003-09-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample Text

Author : Corrado De Concini
Publisher : American Mathematical Soc.
ISBN 13 : 147044187X
Total Pages : 153 pages
Book Rating : 4.76/5 ( download)

DOWNLOAD NOW!

Download or read book The Invariant Theory of Matrices written by Corrado De Concini and published by American Mathematical Soc.. This book was released on 2017-11-16 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Igor Dolgachev
Publisher :
ISBN 13 : 9781107367173
Total Pages : 236 pages
Book Rating : 4.74/5 ( download)

DOWNLOAD NOW!

Download or read book Lectures on Invariant Theory written by Igor Dolgachev and published by . This book was released on 2003 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.

Author : Marcos Marino
Publisher : Springer
ISBN 13 : 3540798145
Total Pages : 219 pages
Book Rating : 4.49/5 ( download)

DOWNLOAD NOW!

Download or read book Enumerative Invariants in Algebraic Geometry and String Theory written by Marcos Marino and published by Springer. This book was released on 2008-08-15 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 981277078X
Total Pages : 446 pages
Book Rating : 4.83/5 ( download)

DOWNLOAD NOW!

Download or read book Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory written by Jian-Shu Li and published by World Scientific. This book was released on 2007 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : P. E. Newstead
Publisher : Alpha Science International Limited
ISBN 13 : 9788184871623
Total Pages : 166 pages
Book Rating : 4.27/5 ( download)

DOWNLOAD NOW!

Download or read book Introduction to Moduli Problems and Orbit Spaces written by P. E. Newstead and published by Alpha Science International Limited. This book was released on 2012 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.