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 $\mathbb{C}{P}^1$ has a single singular fiber. The case when the fiber at infinity is of type $I_0^{\ast }$ is further analyzed, and we give constructions of all the possible configurations of singular curves inelliptic fibrations having this type of singular fiber at infinity.

References in corpus (5)

• Twisted wild character varieties
• Topology of Hitchin systems and Hodge theory of character varieties: the case A_1
• The birational geometry of irregular Higgs bundles
• Two-dimensional moduli spaces of irregular Higgs bundles
• Perversity equals weight for Painlevé spaces