Intersection Pairings on Quotients and Moduli Spaces, and Witten’s Nonabelian Localization

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Many moduli spaces in complex algebraix geometry can be expressed as quotients, in the sense of Mumford’s geometric invariant theory [18], of nonsingular complex projective varieties X by actions of complex reductive groups G. Any such quotient can also be identified with a symplectic quotient (or Marsden-Weinstein reduction) of the variety X by a maximal compact subgroup K of the reductive group G [14], [18], [19]. This symplectic quotient is µ-1(0)/K, where µ : X → k* is a moment map for the action of K on X equipped with a suitable symplectic form.