A note on unfolding manifolds of meromorphic connections on the Riemann sphere with unramified singularities

TL;DR

This paper introduces a Poisson manifold construction that models deformations of moduli spaces of meromorphic connections with unramified irregular singularities, linking unfolding of singularities to geometric structures.

Contribution

It presents a novel Poisson manifold framework capturing deformations of moduli spaces related to unramified irregular singularities in meromorphic connections.

Findings

Construction of a Poisson manifold for deformation of moduli spaces

Link between unfolding irregular singularities and geometric structures

Foundation for future detailed results in forthcoming paper

Abstract

This note explains a construction of a Poisson manifold whose symplectic foliation describes a deformation of a moduli space of meromorphic connections with unramified irregular singularities. In particular, this deformation of the moduli space corresponds to the unfolding of irregular singularities of the meromorphic connections. This is an announcement of some results in the forthcoming paper.