Chapter 0.Preliminaries
1.Definitions
2.First properties
3.Good and bad actions
4.Further properties
5.Resume of some results of GRorrHENDIECK
Chapter 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
Chapter 2.Analysis of stability
1.A numeral criterion
2.The fiag complex
3.Applications
Chapter 3.An elementary example
1.Pre-stability
2．Stability
Chapter 4.Further examples
1.Binary quantics
2.Hypersurfaces
3.Counter-examples
4.Sequences of linear subspaces
5.The projective adjoint action
6.Space curves
Chapter 5.The problem of moduli-18t construction
1.General discussion
2.Moduli as an orbit space
3.First chern classes
4.Utilization of 4.6
Chapter 6.Abelian， schemes
1．Duals
2.Polarizations
3.Deformations
Chapter 7.The method of covan：ants-2nd construction
1.The technique
2.Moduli as an orbit space
3.The covariant
4.Application to curves
Chapter 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
Appendix to Chapter 1
Appendix to Chapter 2
Appendix to Chapter 3
Appendix to Chapter 4
Appendix to Chapter 5
Appendix to Chapter 7
References
Index of definitions and notations
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