Topological aspects of chow quotients

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9 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)399-440
Number of pages42
JournalJournal of Differential Geometry
Issue number3
StatePublished - 2005

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology


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