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arXiv · 0812.2782

Symplectic implosion and non-reductive quotients

Frances Kirwan
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Abstract

The symplectic implosion construction of Guillemin, Jeffrey and Sjamaar associates to a Hamiltonian action of a compact group K on a symplectic manifold X its 'imploded cross section'. When X is a complex projective variety and K acts linearly on X, this construction is closely related to geometric invariant theory (GIT) for the action on X of a maximal unipotent subgroup U of the complexification G of K. The aim of this paper is to generalise symplectic implosion to give a symplectic construction for GIT-like quotients by unipotent radicals U of arbitrary parabolic subgroups P of the complex reductive group G acting linearly on the projective variety X.

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Frances Kirwan. 2008-12-15. Symplectic implosion and non-reductive quotients. https://arxiv.org/abs/0812.2782

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