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Title:
Hilb T*C and Higgs bundles
Speaker:
Abstract:
We will discuss analogies between the moduli space M of Higgs bundles over a curve C and the Hilbert scheme Hilb T*C of points on the cotangent bundle of the curve C. An Higgs field over a curve C is the data of a vector bundle and a twisted endomorphism of it. Taking the characteristic polynomial of the endomorphism gives a proper Lagrangian fibration of M, whose generic fiber is a Jacobian variety. This leads to a birational map from M to Hilb T*C. We will concentrate on the case where C is an elliptic curve. Here things are better behaved, and, taking into account a parabolic structure on the Higgs bundles, it is possible to extend the birational map to an actual isomorphism. This is achieved thanks to a Fourier-Mukai transform analysis. The talk is based on Nakajima's book and on an article of M. Groechenig.
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