Algebraic Nahm transform for Parabolic Higgs Bundles on P^1
Algebraic Geometry
2014-12-17 v2
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 blow-up. Finally, we prove the main properties of the induced map on moduli spaces: involutibility and preservation of the hyper-Kaehler structure.
Keywords
Cite
@article{arxiv.math/0610301,
title = {Algebraic Nahm transform for Parabolic Higgs Bundles on P^1},
author = {K. Aker and Sz. Szabo},
journal= {arXiv preprint arXiv:math/0610301},
year = {2014}
}
Comments
55 pages, AmsLaTex, uses smfart