English

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