Calabi-Yau orbifolds over Hitchin bases

In recent years, it has been realized that some Hitchin systems are closely related to certain quasi-projective Calabi-Yau threefolds. The former is an algebraic integrable system defined on the moduli space of G-Higgs bundles over a compact Riemann surface where G is a simple complex Lie group. It maps to the Hitchin base via the Hitchin map/fibration. The relation to quasi-projective Calabi-Yau threefolds over Hitchin bases was so far only understood when the Dynkin diagram of G is of type ADE.

In this talk, we will construct Calabi-Yau orbifolds over Hitchin bases and relate them to G-Hitchin systems without restriction on the Dynkin diagram of G.