Algebraic Nahm transform for Parabolic Higgs Bundles on P1
K. Aker, Sz. Szabo
Abstract
We study Nahm transformation for parabolic Higgs bundles on the projective line 1, with logarithmic singularities on a finite set P. Such a Higgs bundle can be given by its spectral data: a Hirzebruch surface Z together with a coherent sheaf M on Z, supported in dimension 1 and away from infinity. We describe the transform in terms of these data. The main technical tool is the notion of proper transform of a coherent sheaf with respect to a blow-up. Finally, we prove the main properties of the induced map on moduli spaces: involutibility and preservation of the hyper-Kaehler structure.
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