Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 085, 28 pages      arXiv:1808.10125      https://doi.org/10.3842/SIGMA.2019.085

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

Péter Ivanics ^a, András I. Stipsicz ^a and Szilárd Szabó ^b
a) Rényi Institute of Mathematics, 1053 Budapest, Reáltanoda utca 13-15, Hungary
^b) Budapest University of Technology and Economics, 1111 Budapest, Egry József utca 1, H épület, Hungary

Received February 02, 2019, in final form October 25, 2019; Published online November 04, 2019

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.

Key words: irregular Higgs bundles; Hitchin fibration; elliptic fibrations.

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