Regular Strata and Moduli Spaces of Irregular Singular Connections

Abstract

In joint work with C. Bremer, the author has developed a geometric theory of fundamental strata which provides a new approach to the study of meromorphic G-connections on curves (for complex reductive G). In this theory, a fundamental stratum associated to a connection at a singular point plays the role of the local leading term of the connection. In this paper, we illustrate this theory for $G = \mathfrak{g}\mathfrak{l}_{2}(\mathbb{C})$ (i.e. for connections on rank two vector bundles). In particular, we show how this approach can be used to construct explicit moduli spaces of irregular singular connections on the projective line with specified singularities and formal types.