Closed orbits and uniform $S$-instability in geometric invariant theory

Closed Orbits and Uniform S-instability in Invariant Theory

In this paper we consider various problems involving the action of a reductive group G on an affine variety V . We prove some general rationality results about the G-orbits in V . In addition, we extend fundamental results of Kempf and Hesselink regarding optimal destabilizing parabolic subgroups of G for such general G-actions. We apply our general rationality results to answer a question of S...

No : 1 Title : ‘ Closed Orbits and Uniform S - Instability in Geometric Invariant Theory

In this paper we consider various problems involving the action of a reductive group G on an affine variety V . We prove some general rationality results about the G-orbits in V . In addition, we extend fundamental results of Kempf and Hesselink regarding optimal destabilizing parabolic subgroups of G for such general G-actions. We apply our general rationality results to answer a question of S...

Construction of Invariant Tori around Closed Orbits

The approach and methods introduced by McGill & Binney and Kaasalainen & Binney (Papers I and III), for the construction of phase-space tori that are approximate invariant tori of a given Hamiltonian, are generalized to include motion`trapped' around general closed orbits. This is accomplished by introducing point transformations that map the connguration space around a closed orbit in the targ...

Basic geometric invariant theory

Geometric invariant theory and flips

Ever since the invention of geometric invariant theory, it has been understood that the quotient it constructs is not entirely canonical, but depends on a choice: the choice of a linearization of the group action. However, the founders of the subject never made a systematic study of this dependence. In light of its fundamental and elementary nature, this is a rather surprising gap, and this pap...