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Author Mumford, David, 1937-

Title Geometric invariant theory / D. Mumford, J. Fogarty, F. Kirwan.

Published Berlin ; New York : Springer-Verlag, c1994.

Copies

Location Call No. Status
 UniM ERC  516.35 MUMF    AVAILABLE
Edition 3rd enl. ed.
Physical description xiv, 292 p. : ill. ; 24 cm.
Series Ergebnisse der Mathematik und ihrer Grenzgebiete ; 34
Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 34.
Notes Previous ed.: 1982.
Bibliography Includes bibliographical references (p. [253]-290) and index.
Contents Ch. 0. Preliminaries. 1. Definitions. 2. First properties. 3. Good and bad actions. 4. Further properties. 5. Resume of some results of Grothendieck -- Ch. 1. Fundamental theorems for the actions of reductive groups. 1. Definitions. 2. The affine case. 3. Linearization of an invertible sheaf. 4. The general case. 5. Functional properties -- Ch. 2. Analysis of stability. 1. A numeral criterion. 2. The flag complex. 3. Applications -- Ch. 3. An elementary example. 1. Pre-stability. 2. Stability -- Ch. 4. Further examples. 1. Binary quantics. 2. Hypersurfaces. 3. Counter-examples. 4. Sequences of linear subspaces. 5. The projective adjoint action. 6. Space curves -- Ch. 5. The problem of moduli - 1st construction. 1. General discussion. 2. Moduli as an orbit space. 3. First chern classes. 4. Utilization of 4.6 -- Ch. 6. Abelian schemes. 1. Duals. 2. Polarizations. 3. Deformations -- Ch. 7. The method of covariants - 2nd construction. 1. The technique. 2. Moduli as an orbit space. 3. The covariant.
Contents note continued: 4. Application to curves -- Ch. 8. The moment map. 1. Symplectic geometry. 2. Symplectic quotients and geometric invariant theory. 3. Kahler and hyperkahler quotients. 4. Singular quotients. 5. Geometry of the moment map. 6. The cohomology of quotients: the symplectic case. 7. The cohomology of quotients: the algebraic case. 8. Vector bundles and the Yang-Mills functional. 9. Yang-Mills theory over Riemann surfaces.
Other author Fogarty, John, 1934-
Kirwan, Frances Clare, 1959-
Subject Geometry, Algebraic.
Invariants.
Moduli theory.
ISBN 3540569634 (Berlin : acid-free paper)
9783540569633 (Berlin)
0387569634 (New York : acid-free paper)