The complexity of the singular fibers of the Hitchin system stems from the diversity of singularities of spectral curves. Already for G=GL(2,C) all singularities of type A appear. In light of the Deligne-Mumford compactification of the moduli space of smooth projective curves, it is a natural idea to compactify the family of smooth spectral curves over the regular locus of the Hitchin base to a family of nodal curves over a modified Hitchin base. In the talk, I will compare several approaches to achieve this goal in the GL(2,C)-case. These motivate the consideration of the moduli space of quadratic multi-scale differentials with simple zeroes as modified Hitchin base. I will conclude by formulating a spectral correspondence in this context. This is joint work with Martin Möller.
Goethe-Universität in Frankfurt am Main
Geometry and Topology