Symplectic moduli space of 1-dimensional sheaves on Poisson surfaces

TL;DR

This paper demonstrates that the Poisson structure on the smooth part of a moduli space of 1-dimensional sheaves on a Poisson surface can be derived from a natural symplectic structure, revealing deep geometric connections.

Contribution

It establishes that the Poisson structure on the moduli space is a reduction of an inherent symplectic structure, linking Poisson and symplectic geometry in this context.

Findings

Poisson structure is a reduction of a natural symplectic structure

Results apply to moduli spaces on Poisson projective surfaces

Provides geometric insight into the structure of sheaf moduli spaces

Abstract

We show that the Poisson structure on the smooth locus of a moduli space of 1-dimensional sheaves on a Poisson projective surface $X$ over $\mathbb C$ is a reduction of a natural symplectic structure.