Topological aspects of Chow quotients

Abstract

This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to introduce the Perturbation–Translation–Specialization relation that gives a computable characterization of the Chow cycles of the Chow quotient. Also, we provide, in the languages that are familiar to topologists and differential geometers, many topological interpretations of Chow quotient that have the advantage to be more intuitive and geometric. More precisely, over the field of complex numbers, these interpretations are, symplectically, the moduli spaces of stable orbits with prescribed momentum charges; and topologically, the moduli space of stable action-manifolds.