Algebraic Nahm transform for Parabolic Higgs Bundles on P^1
Abstract
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 blowup. Finally, we prove the main properties of the induced map on moduli spaces: involutibility and preservation of the hyperKaehler structure.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 2006
 DOI:
 10.48550/arXiv.math/0610301
 arXiv:
 arXiv:math/0610301
 Bibcode:
 2006math.....10301A
 Keywords:

 Mathematics  Algebraic Geometry;
 14H60;
 14F05;
 14E05;
 14J26
 EPrint:
 55 pages, AmsLaTex, uses smfart