Geometric invariances

Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebie-te, second edition, Springer-Verlag, New York Heidelberg Berlin 1982. 

First we need some generalities on the relationship between the geometric invariant theory and the moment map. General reference of this section is [60, Chapter 8]. (See also [71] for reference to the geometric invariant theory.)... 

This function plays a fundamental role in the relationship between the moment map and the geometric invariant theory as seen in the following proposition. 

D. Mumford, J. Fogarty and F. Kirwan, Geometric invariant theory. Third Enlarged Edition ,... 

When X = C2, X can be identified with the set of GLJl(C)-orbits of (Hi, B2, i) where Bi, B2 are commuting n x n-matrices and i is a cyclic vector (Theorem 1.14). Many properties of (C2) are derived from this description. In Chapter 3, we shall regard the description as a geometric invariant theory quotient and a hyper-Kahler quotient. This description is very similar to the definition of quiver varieties which were studied in [62]. 

Mumford, D. Geometric Invariant Theory (New York Springer, 1965). 

GIT] D. Mumford, Geometric invariant theory, second enlarged edition. Ergebnisse der Mathematik und ihrer Grenzgebiete 34, Springer-Veriag (1982). 

Zhu, H.Y. and Klein, D.J. (1996a). Graph-Geometric Invariants for Molecular Structures. J.Chem.lnf.Comput.ScL, 36,1067-1075. 

Goldman, B.B. and Wipke, W.T. (2000) Quadratic shape descriptors. 1. Rapid superposition of dissimilar molecules using geometrically invariant surface descriptors. J. Chem. Inf. Comput. Sci, 40, 644-658. 

In general relativity, where the relative motion between frames is not inertial, the geometric invariant of the resulting curved spacetime is... 

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