The Singular Fiber of the Hitchin Map

@article{Gothen2013TheSF,
  title={The Singular Fiber of the Hitchin Map},
  author={P. Gothen and Andr'e Oliveira},
  journal={International Mathematics Research Notices},
  year={2013},
  volume={2013},
  pages={1079-1121}
}
Given any line bundle L of positive degree, on a compact Riemann surface, let $M_L^\Lambda$ be the moduli space of L-twisted Higgs pairs of rank 2 with fixed determinant isomorphic to $\Lambda$ and traceless Higgs field. We give a description of the singular fibre of the Hitchin map $H:M^L_\Lambda\to H^0(L^2)$, 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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