Lectures on Invariant Theory

Lectures on Invariant Theory
Title Lectures on Invariant Theory PDF eBook
Author Igor Dolgachev
Publisher Cambridge University Press
Pages 244
Release 2003-08-07
Genre Mathematics
ISBN 9780521525480

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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
Title Invariant Theory PDF eBook
Author T.A. Springer
Publisher Springer
Pages 118
Release 2006-11-14
Genre Mathematics
ISBN 3540373705

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The Theory of Algebraic Number Fields

The Theory of Algebraic Number Fields
Title The Theory of Algebraic Number Fields PDF eBook
Author David Hilbert
Publisher Springer Science & Business Media
Pages 360
Release 2013-03-14
Genre Mathematics
ISBN 3662035456

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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.

An Introduction to Invariants and Moduli

An Introduction to Invariants and Moduli
Title An Introduction to Invariants and Moduli PDF eBook
Author Shigeru Mukai
Publisher Cambridge University Press
Pages 528
Release 2003-09-08
Genre Mathematics
ISBN 9780521809061

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Sample Text

Enumerative Invariants in Algebraic Geometry and String Theory

Enumerative Invariants in Algebraic Geometry and String Theory
Title Enumerative Invariants in Algebraic Geometry and String Theory PDF eBook
Author Marcos Marino
Publisher Springer
Pages 219
Release 2008-08-15
Genre Mathematics
ISBN 3540798145

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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.

Symmetry, Representations, and Invariants

Symmetry, Representations, and Invariants
Title Symmetry, Representations, and Invariants PDF eBook
Author Roe Goodman
Publisher Springer Science & Business Media
Pages 731
Release 2009-07-30
Genre Mathematics
ISBN 0387798528

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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.

Lectures on the Topology of 3-manifolds

Lectures on the Topology of 3-manifolds
Title Lectures on the Topology of 3-manifolds PDF eBook
Author Nikolai Saveliev
Publisher Walter de Gruyter
Pages 220
Release 1999
Genre Mathematics
ISBN 9783110162721

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