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Cohomology pairings on singular quotients in geometric invariant theory

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Abstract

In this paper we shall give formulas for the pairings of intersection cohomology classes of complementary dimensions in the intersection cohomology of geometric invariant-theoretic quotients for which semistability is not necessarily the same as stability (although we make some weaker assumptions on the action). We also give formulas for intersection pairings on resolutions of singularities (or more precisely partial resolutions, since orbifold singularities are allowed) of the quotients.

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Authors and Affiliations

  1. Mathematics Department, University of Toronto, Toronto, ON M5S 3G3, Canada

    Lisa C. Jeffrey

  2. Department of Mathematics, Seoul National University, Seoul 151-747, Korea

    Young-Hoon Kiem

  3. Balliol College, Oxford OX1 3BJ, UK

    Frances Kirwan

  4. Christ's College, Cambridge, CB2 3BU, UK

    Jonathan Woolf

Authors
  1. Lisa C. Jeffrey
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  2. Young-Hoon Kiem
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  3. Frances Kirwan
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  4. Jonathan Woolf
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Corresponding authors

Correspondence to Lisa C. Jeffrey, Young-Hoon Kiem, Frances Kirwan or Jonathan Woolf.

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Jeffrey, L., Kiem, YH., Kirwan, F. et al. Cohomology pairings on singular quotients in geometric invariant theory. Transformation Groups 8, 217–259 (2003). https://doi.org/10.1007/s00031-003-0510-y

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  • DOI: https://doi.org/10.1007/s00031-003-0510-y

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