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We give a complete description of the two-dimensional moduli spaces of stableHiggs bundles of rank 2 over complex projective line with one irregularsingular point, having a regular leading-order term, and endowed with a genericcompatible parabolic structure such that the parabolic degree of the Higgsbundle is 0. Our method relies on elliptic fibrations of the rational ellipticsurface, an equivalence of categories between irregular Higgs bundles and somesheaves on a ruled surface, and an analysis of stability conditions.

Two-dimensional moduli spaces of irregular Higgs bundles