Symplectic implosion and non-reductive quotients
Algebraic Geometry
2008-12-16 v1 Symplectic Geometry
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.
Cite
@article{arxiv.0812.2782,
title = {Symplectic implosion and non-reductive quotients},
author = {Frances Kirwan},
journal= {arXiv preprint arXiv:0812.2782},
year = {2008}
}
Comments
For the proceedings of the 65th birthday conference for Hans Duistermaat, Utrecht 2007