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Description: |
A Hitchin pair on a complex projective curve consists of a vector bundle and an endomorphism of this bundle, twisted by a fixed line bundle L. Thus, when L is the canonical bundle of the curve, a Hitchin pair is a Higgs bundle. There is a Hitchin map from the moduli space of Hitchin pairs to an affine space, defined by taking the characteristic polynomial of the endomorphism. The generic fibre of the Hitchin map is an abelian variety, while the fibre over zero is the so-called nilpotent cone, which encodes the topology of the moduli space. Using the spectral curve construction we study the intermediate singular fibres of the Hitchin map in the case of rank 2 fixed determinant Hitchin pairs. In particular we show that these fibres are connected. The talk is based on joint work with André Gama Oliveira.
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