Given any line bundle L of positive degree, on a compact Riemann surface, let MLΛ 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:MΛL→H0(L2)
Nearby in the stack
, when the corresponding spectral curve has any singularity of type
Am−1
. In particular, we prove directly that this fibre is connected.