We define and parametrise so-called sl(2)-type fibres of the Sp(2n,C)- and SO(2n+1,C)
Nearby in the stack
-Hitchin system. These are (singular) Hitchin fibres, where the spectral curve induces a two-sheeted covering of a second Riemann surface
Y
. This identifies the
sl(2)
-type Hitchin fibres with fibres of an
SL(2,C)
- respectively
PSL(2,C)
-Hitchin map on
Y
. We give a stratification of these singular spaces by semi-abelian spectral data, study their irreducible components and obtain a global description of the first degenerations. Comparing the semi-abelian spectral data of
sl(2)
-type Hitchin fibres for the two Langlands dual groups, we extend the well-known Langlands duality of regular Hitchin fibres to
sl(2)
-type Hitchin fibres. Finally, we construct solutions to the decoupled Hitchin equation for Higgs bundles of
sl(2)
-type. We conjecture these to be limiting metrics along rays to the ends of the moduli space.