Topological Aspects of Chow Quotients

Details Topological Aspects of Chow Quotients Topological Aspects of Chow Quotients

2003-08-04

arxiv.org/abs/math/0308027v4

Mathematics

Algebraic Geometry

36 pages. Improved version. Introduction was completely rewritten with five newly added figures to help to illustrate the idea

Scientific paper

This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to give some topological interpretations and characterization of Chow quotient which have the advantage to be more intuitive and geometric. This is to be done over the field of complex numbers and in the languages that are familiar to topologists and differential geometers. More precisely, the main observation of this paper is that, over the field of complex numbers, the Chow quotient admits symplectic and other topological interpretations, namely, symplectically, the moduli spaces of stable orbits with prescribed momentum charges; and topologically, the moduli space of stable action-manifolds. In addition, we give a computable characterization of the Chow cycles of the Chow quotient, using the so-called perturbing-translating-specializing relation.

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