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

Frances Kirwan
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Frances Kirwan: Balliol College

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 491-497 from Springer

Abstract: Abstract 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.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_42

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