芒福德编著的《几何不变量理论》内容介绍：This edition of the book has been extended to take account of one of these developments， one which was just hinted at in the second edition. A close and very fruitful relationship has been discovered between geometric invariant theory for quasi projective complex varieties and the moment map in Symplectic geometry， and a chapter has been added describing this relationship and some of its applications. In an infinite-dimensional setting the moment map links geometric invariant theory and Yang-Mills theory， which has of course been the focus of much attention among mathematicians over the last fifteen years.

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