Symplectic implosion and non-reductive quotients
Abstract
Description
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.
For the proceedings of the 65th birthday conference for Hans Duistermaat, Utrecht 2007
For the proceedings of the 65th birthday conference for Hans Duistermaat, Utrecht 2007