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

TL;DR

This paper classifies the singular fibers of Hitchin fibrations on 2D moduli spaces of irregular Higgs bundles over the complex projective line, providing detailed descriptions and constructions for specific fiber types.

Contribution

It completely characterizes the four cases with a single singular fiber and constructs all configurations for the type I_0^* fiber at infinity.

Findings

Four cases of singular fibers identified and described.

Explicit constructions for configurations with an I_0^* fiber.

Enhanced understanding of irregular Higgs bundle moduli spaces.

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 $I_0^*$ 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.