Two-dimensional moduli spaces of rank 2 Higgs bundles over \(\mathbb{C} \mathbb P^1\) with one irregular singular point
The aim of this paper is to give a complete description of the two-dimensional moduli spaces of stable Higgs bundles of rank 2 over \(\mathbb{C}\mathbb P^1\) with one irregular singular point, having a regular leading-order term, and endowed with a generic compatible parabolic structure such that the parabolic degree of the Higgs bundle is 0. The method used relies on elliptic fibrations of the rational elliptic surface, an equivalence of categories between irregular Higgs bundles and some sheaves on a ruled surface, and an analysis of stability conditions. This paper is organized as follows: The first section is an introduction to the subject. In the second section the authors fix their notations and recall some well-known background material used in the paper. In Section 3 the authors give a detailed analysis of elliptic fibrations on the rational elliptic surface with one singular fiber of type \(\widetilde{E}_7\) or of type \(\widetilde{E}_8\). In section 4, the authors study singular fibers of elliptic fibrations on rational elliptic surfaces. Section 5 is devoted to the study of stability analysis in the untwisted case while section 6 is devoted to the twisted case.
scientific article; zbMATH DE number 6881415
scientific article