Dolgachev, Igor,
Lectures on Invariant Theory / Igor Dolgachev. - Cambridge : Cambridge University Press, 2003. - 1 online resource (238 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 296 . - London Mathematical Society Lecture Note Series ; no. 296. .
Title from publisher's bibliographic system (viewed on 16 Oct 2015).
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.
9780511615436 (ebook)
Invariants
Linear algebraic groups
Geometry, Differential
Geometry, Algebraic
QA201 / .D65 2002
512.5
Lectures on Invariant Theory / Igor Dolgachev. - Cambridge : Cambridge University Press, 2003. - 1 online resource (238 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 296 . - London Mathematical Society Lecture Note Series ; no. 296. .
Title from publisher's bibliographic system (viewed on 16 Oct 2015).
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.
9780511615436 (ebook)
Invariants
Linear algebraic groups
Geometry, Differential
Geometry, Algebraic
QA201 / .D65 2002
512.5