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Implosion for hyperkähler manifolds

Part of: Global differential geometry Algebraic groups Symplectic geometry, contact geometry

Published online by Cambridge University Press:  28 June 2013

Andrew Dancer ,
Frances Kirwan  and
Andrew Swann
Andrew Dancer
Affiliation:
Jesus College, Oxford, OX1 3DW, UK email dancer@maths.ox.ac.uk
Frances Kirwan
Affiliation:
Balliol College, Oxford, OX1 3BJ, UK email kirwan@maths.ox.ac.uk
Andrew Swann
Affiliation:
Department of Mathematics, Aarhus University, Ny Munkegade 118, Bldg 1530, DK-8000 Aarhus C, Denmark email swann@imf.au.dk CP3-Origins, Centre of Excellence for Cosmology and Particle Physics Phenomenology, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark email swann@imf.au.dk
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Abstract

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We introduce an analogue in hyperkähler geometry of the symplectic implosion, in the case of $\mathrm{SU} (n)$ actions. Our space is a stratified hyperkähler space which can be defined in terms of quiver diagrams. It also has a description as a non-reductive geometric invariant theory quotient.

Keywords

symplectic implosionquiver diagramhyperkähler quotientnon-reductive geometric invariant theoryKostant variety

MSC classification

Secondary: 53C26: Hyper-Kähler and quaternionic Kähler geometry, “special” geometry 53D20: Momentum maps; symplectic reduction 14L24: Geometric invariant theory
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 9 , September 2013 , pp. 1592 - 1630
Copyright
© The Author(s) 2013 

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