Poisson structures and birational morphisms associated with bundles on elliptic curves

TL;DR

This paper introduces a Poisson structure on moduli spaces of principal G-bundles on elliptic curves and explores birational morphisms between related projective spaces, advancing understanding of their geometric properties.

Contribution

It defines a new Poisson structure on moduli spaces of principal G-bundles on elliptic curves and investigates birational morphisms between these spaces.

Findings

Established a Poisson structure on moduli spaces related to elliptic curves.

Analyzed birational morphisms between projective spaces as moduli spaces.

Provided insights into the geometric relationships of these moduli spaces.

Abstract

In this paper we define a Poisson structure on some moduli spaces related to principal G-bundles on elliptic curves, the simplest example being the moduli space of stable pairs: a vector bundle and its global section. We also study birational morphisms between projective spaces appearing as such moduli spaces.