Poisson structure on the moduli spaces of sheaves of pure dimension one on a surface
Algebraic Geometry
2019-08-23 v1
Abstract
Let S be a smooth complex projective surface equipped with a Poisson structure s and also a polarization H. The moduli space M_H(S,P) of stable sheaves on S having a fixed Hilbert polynomial P of degree one has a natural Poisson structure given by s, studied by Tyurin and Bottacin. We prove that the symplectic leaves of M_H(S,P) are the fibers of the natural map from it to the symmetric power of the effective divisor on S given by the singular locus of s.
Keywords
Cite
@article{arxiv.1908.08260,
title = {Poisson structure on the moduli spaces of sheaves of pure dimension one on a surface},
author = {Indranil Biswas and Tomas L. Gomez},
journal= {arXiv preprint arXiv:1908.08260},
year = {2019}
}
Comments
8 pages