Moduli spaces of meromorphic connections and quiver varieties

TL;DR

This paper links moduli spaces of meromorphic connections on the Riemann sphere with Nakajima's quiver varieties, providing new insights into the irregular Deligne-Simpson problem.

Contribution

It establishes a correspondence between moduli spaces of meromorphic connections and quiver varieties, advancing the understanding of irregular singularities.

Findings

Moduli spaces are described as Nakajima's quiver varieties.

Partial solution to the additive irregular Deligne-Simpson problem.

Provides a geometric framework for irregular connections.

Abstract

We describe the moduli spaces of meromorphic connections on trivial holomorphic vector bundles over the Riemann sphere with at most one (unramified) irregular singularity and arbitrary number of simple poles as Nakajima's quiver varieties. This result enables us to solve partially the additive irregular Deligne-Simpson problem.