Algebraic Nahm transform for Parabolic Higgs Bundles on P^1

Details Algebraic Nahm transform for Parabolic Higgs Bundles on P^1 Algebraic Nahm transform for Parabolic Higgs Bundles on P^1

2006-10-09

arxiv.org/abs/math/0610301v2

Mathematics

Algebraic Geometry

55 pages, AmsLaTex, uses smfart

Scientific paper

We study Nahm transformation for parabolic Higgs bundles on the projective line \PP^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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