On the cohomology of hyperkahler quotients
Lisa Jeffrey, Young-Hoon Kiem, Frances Kirwan
TL;DR
This paper develops a partial desingularisation method and a surjectivity criterion for the cohomology of hyperk"ahler quotients, with applications to linear actions on hyperk"ahler vector spaces.
Contribution
It introduces a new desingularisation construction and a criterion for the surjectivity of the Kirwan map in the hyperk"ahler setting.
Findings
Established a partial desingularisation construction.
Provided a surjectivity criterion for the hyperk"ahler Kirwan map.
Applied the criterion to linear hyperk"ahler actions.
Abstract
This paper gives a partial desingularisation construction for hyperk\"ahler quotients and a criterion for the surjectivity of an analogue of the Kirwan map to the cohomology of hyperk\"ahler quotients. This criterion is applied to some linear actions on hyperk\"ahler vector spaces.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Topics in Algebra · Algebraic structures and combinatorial models