Geometric invariant theory.
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Geometric invariant theory. by David Mumford

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Published by Springer-Verlag in Berlin, New York .
Written in English

Subjects:

  • Geometry, Algebraic.,
  • Invariants.

Book details:

Edition Notes

Bibliography: p. [144]-145.

SeriesErgebnisse der Mathematik und ihrer Grenzgebiete, n.F.,, Bd. 34
Classifications
LC ClassificationsQA564 .M85
The Physical Object
Paginationv, 145 p.
Number of Pages145
ID Numbers
Open LibraryOL5945258M
LC Control Number65016690
OCLC/WorldCa549870

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Geometric Invariant Theory. 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.5/5. Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. Geometric Invariant Theory (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge): David Mumford, John Fogarty, Frances Kirwan: : Books. Enter your mobile number or email address below and we'll send you a link to download the free Kindle by: Geometric Invariant Theory - David Mumford, John Fogarty - Google Books. 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.

Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry. The next result, due to Hilbert, justi es the importance of reductive groups in geometric invariant theory. 1. 2 JOS E SIMENTAL Theorem Let Gbe a reductive group acting on an a ne algebraic variety X. Then, the algebra of invariants C[X]G is nitely generated. Proof. First we reduce to the case when X= V, a representation of G. MODULI SPACES AND INVARIANT THEORY 5 [Mu]S. Mukai, An introduction to Invariants and Moduli [M1]D. Mumford, Curves and their Jacobians [M2]D. Mumford, Geometric Invariant Theory [MS]D. Mumford, K. Suominen, Introduction to the theory of moduli [PV]V. Popov, E. Vinberg, Invariant TheoryFile Size: 2MB.   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 Brand: Springer Berlin Heidelberg.

"Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in , a second, enlarged editonappeared in ) is the standard reference on applicationsof invariant theory to 5/5(1). The term geometric invariant theory (GIT) is due to Mumford and is the title of his foundational book [Mu]. This amazing work began with an explanation of how a group scheme acts on a scheme and lays the foundation necessary for the difficult theory in positive characteristic. geometric invariant theory introduced by Mumford in the ’s, and the notion of symplectic quotient introduced by Meyer and Marsden-Weinstein in the ’s. Geometric invariant theory (GIT) is a method for constructing group quotients in algebraic geometry and it is frequently used to construct moduli spaces. The core of this course is the construction of GIT quotients.