TY  - BOOK
AU  - Mumford, D.
AU  - Fogarty, J.
AU  - Kirwan, F.
TI  - Geometric invariant theory
SN  - 3540569634
U1  - 516.35 
PY  - 1994///
CY  - Berlin
PB  - Springer-Verlag
KW  - Algebraic Geometry
KW  - Invariants
KW  - Moduli theory
N1  - Preliminaries --
1. Definitions --
2. First properties --
3. Good and bad actions --
4. Further properties --
5. Resume of some results of Grothendieck --
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 --
Analysis of stability --
1. A numeral criterion --
2. The flag complex --
3. Applications --
An elementary example --
1. Pre-stability --
2. Stability --
4. Further examples --
1. Binary quantics --
2. Hypersurfaces --
3. Counter-examples --
4. Sequences of linear subspaces --
5. The projective adjoint action --
6. Space curves --
The problem of moduli --
1st construction --
1. General discussion --
2. Moduli as an orbit space --
3. First chern classes --
4. Utilization of 4.6 --
Abelian schemes --
1. Duals --
2. Polarizations --
3. Deformations --
The method of covariants --
2nd construction --
1. The technique --
2. Moduli as an orbit space --
3. The covariant --
4. Application to curves --
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
ER  -