Hitchin fibrations on moduli of irregular Higgs bundles and motivic wall-crossing

TL;DR

This paper provides a comprehensive analysis of the Hitchin fibration for rank 2 irregular Higgs bundles with two poles, exploring singular fibers and motivic wall-crossing phenomena related to eigenvalues and parabolic weights.

Contribution

It offers a complete description of the Hitchin fibration on all 2D moduli spaces of irregular Higgs bundles with two poles, including the dependence on eigenvalues and wall-crossing behavior.

Findings

Classification of singular fibers in the Hitchin fibration

Description of motivic wall-crossing phenomena

Dependence of fiber structure on eigenvalues and weights

Abstract

In this paper we give a complete description of the Hitchin fibration on all 2-dimensional moduli spaces of rank 2 irregular Higgs bundles with two poles on the projective line. We describe the dependence of the singular fibers of the fibration on the eigenvalues of the Higgs fields, and describe the corresponding motivic wall-crossing phenomenon in the parameter space of parabolic weights.