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arXiv · 1012.5541

The singular fibre of the Hitchin map

Peter B. Gothen·André Oliveira
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Abstract

Given any line bundle L of positive degree, on a compact Riemann surface, let $M_L^Λ$ be the moduli space of L-twisted Higgs pairs of rank 2 with fixed determinant isomorphic to $Λ$ and traceless Higgs field. We give a description of the singular fibre of the Hitchin map $H:M^L_Λ\to H^0(L^2)$, when the corresponding spectral curve has any singularity of type $A_{m-1}$. In particular, we prove directly that this fibre is connected.

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Peter B. Gothen, André Oliveira. 2012-02-03. The singular fibre of the Hitchin map. https://doi.org/10.1093/imrn%2Frns020

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