Hitchin Fibrations on Two-Dimensional Moduli Spaces of Irregular Higgs Bundles with One Singular Fiber

Abstract

We analyze and completely describe the four cases when the Hitchin fibration on a 2-dimensional moduli space of irregular Higgs bundles over CP¹ has a single singular fiber. The case when the fiber at infinity is of type I₀* is further analyzed, and we give constructions of all the possible configurations of singular curves in elliptic fibrations having this type of singular fiber at infinity.