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Branes on the Hitchin system arising from finite order line bundles

Date: Wednesday, May 30, 2018 14:00 - 16:00
Speaker: André Oliveira (University of Porto)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Tamas Hausel
Lab building west seminar room

Abstract:

I will explain a recent work, together with E. Franco, P. Gothen and A. Pen-Nieto, where we study the fixed loci on the moduli space M of GL(n,C)-Higgs bundles (over a curve) for the action of tensorization by a line bundle of order n. This loci is hyperholomorphic and can be equipped with a hyperholomorphic sheaf, hence is a BBB-brane on M. Such brane is expected to be dual, via mirror symmetry, to a BAA-brane on M, i.e. to a complex Lagrangian subvariety equipped with a flat bundle. We describe such BAA-brane and show that it can described via certain Hecke modifications. Finally we prove the duality statement via explicit Fourier-Mukai transform. It is noteworthy that these branes lie over the singular locus of the Hitchin fibration.
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