  The sextic plane curves that are invariant under the standard action of the
icosahedral group on the projective plane make up a pencil of genus ten curves
(spanned by a sum of six lines and a three times a conic). This pencil was
first considered in a note by R.~M.~Winger in 1925 and is nowadays named after
him.
  We gave this a modern treatment and proved among other things that it
contains essentially every smooth genus ten curve with icosahedral symmetry.
  We here consider the monodromy group and the period map naturally defined by
the icosahedral symmetry. We showed that this monodromy group is a subgroup of
finite index in $\SL_2(\Zds[\sqrt{5}])$ and the period map brings the Winger
pencil to a curve on the Hilbert modular surface
$\SL_2(\Zds[\sqrt{5}])/\Hds^2$.
