Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces
Algebraic Geometry
2008-11-26 v1 High Energy Physics - Theory
Differential Geometry
Symplectic Geometry
Abstract
We give a comparative description of the Poisson structures on the moduli spaces of flat connections on real surfaces and holomorphic Poisson structures on the moduli spaces of holomorphic bundles on complex surfaces. The symplectic leaves of the latter are classified by restrictions of the bundles to certain divisors. This can be regarded as fixing a "complex analogue of the holonomy" of a connection along a "complex analogue of the boundary" in analogy with the real case.
Keywords
Cite
@article{arxiv.math/0009013,
title = {Symplectic geometry on moduli spaces of holomorphic bundles over complex surfaces},
author = {Boris Khesin and Alexei Rosly},
journal= {arXiv preprint arXiv:math/0009013},
year = {2008}
}
Comments
15 pages