The birational geometry of irregular Higgs bundles

Abstract

We give a variant of the Beauville--Narasimhan--Ramanan correspondence for irregular parabolic Higgs bundles with semi-simple irregular part and show that it defines a Poisson isomorphism between certain irregular Dolbeault moduli spaces of a curve and relative Picard bundles of families of ruled surfaces over a curve.

arXiv comment25 pages, improved exposition

References in corpus (3)

• Hyperkahler manifolds and nonabelian Hodge theory of (irregular) curves
• Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry
• Multi-Hamiltonian structures for r-matrix systems

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• Motivic classes of moduli of Higgs bundles and moduli of bundles with connections
• Two-dimensional moduli spaces of irregular Higgs bundles
• Hitchin Fibrations on Two-Dimensional Moduli Spaces of Irregular Higgs Bundles with One Singular Fiber
• Nahm transformation for parabolic integrable connections on the projective line -- case of generic regular graded residues