Lectures on Invariant Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Invariant Theory write by Igor Dolgachev. This book was released on 2003-08-07. Lectures on Invariant Theory available in PDF, EPUB and Kindle. 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
Invariant Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Invariant Theory write by T.A. Springer. This book was released on 2006-11-14. Invariant Theory available in PDF, EPUB and Kindle.
Geometric Invariant Theory and Decorated Principal Bundles
Geometric Invariant Theory and Decorated Principal Bundles - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Invariant Theory and Decorated Principal Bundles write by Alexander H. W. Schmitt. This book was released on 2008. Geometric Invariant Theory and Decorated Principal Bundles available in PDF, EPUB and Kindle. 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.
The Invariant Theory of Matrices
The Invariant Theory of Matrices - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Invariant Theory of Matrices write by Corrado De Concini. This book was released on 2017-11-16. The Invariant Theory of Matrices available in PDF, EPUB and Kindle. 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.
Lectures on Invariant Theory
Lectures on Invariant Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Invariant Theory write by Igor Dolgachev. This book was released on 2003. Lectures on Invariant Theory available in PDF, EPUB and Kindle. This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.
