Author: Jean Alexandre Dieudonné
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 104
Book Description
Invariant Theory, Old and New
Author: Jean Alexandre Dieudonné
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 104
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 104
Book Description
Invariant Theory
Lectures on Invariant Theory
Author: Igor Dolgachev
Publisher: Cambridge University Press
ISBN: 9780521525480
Category : Mathematics
Languages : en
Pages : 244
Book Description
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.
Publisher: Cambridge University Press
ISBN: 9780521525480
Category : Mathematics
Languages : en
Pages : 244
Book Description
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, Old and New. (Reprinted from Advances in Mathematics, Volume 4, Number 1.).
Invariant theory
Invariant Theory
Author: John Fogarty
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 240
Book Description
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 240
Book Description
Invariant Theory
Author: T.A. Springer
Publisher: Springer
ISBN: 3540373705
Category : Mathematics
Languages : en
Pages : 118
Book Description
Publisher: Springer
ISBN: 3540373705
Category : Mathematics
Languages : en
Pages : 118
Book Description
Geometric Invariant Theory
Author: David Mumford
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 248
Book Description
This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 248
Book Description
This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.
Invariant Theory, Old and New [by] Jean A. Dieudonné [and] James B. Carrell
Author: Jean Dieudonné
Publisher:
ISBN:
Category : Invariants
Languages : en
Pages : 85
Book Description
Publisher:
ISBN:
Category : Invariants
Languages : en
Pages : 85
Book Description
Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
Author: Alfonso Zamora Saiz
Publisher: Springer Nature
ISBN: 3030678296
Category : Mathematics
Languages : en
Pages : 127
Book Description
This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.
Publisher: Springer Nature
ISBN: 3030678296
Category : Mathematics
Languages : en
Pages : 127
Book Description
This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry.