Semi-polarized meromorphic Hitchin and Calabi-Yau integrable systems

TL;DR

This paper establishes a new connection between semi-polarized integrable systems arising from meromorphic Hitchin systems of type A and Calabi-Yau threefolds, extending known ADE results to a broader setting.

Contribution

It proves an isomorphism between the moduli space of framed Higgs bundles and a family of Calabi-Yau threefolds' intermediate Jacobians, generalizing Hitchin-Calabi-Yau correspondences.

Findings

The moduli space of framed Higgs bundles forms a semi-polarized integrable system.

Constructed a new family of quasi-projective Calabi-Yau threefolds.

Established an isomorphism between the integrable systems and Calabi-Yau intermediate Jacobians.

Abstract

It was shown by Diaconescu, Donagi and Pantev that Hitchin systems of type ADE are isomorphic to certain Calabi-Yau integrable systems. In this paper, we prove an analogous result in the setting of meromorphic Hitchin systems of type A which are known to be Poisson integrable systems. We consider a symplectization of the meromorphic Hitchin integrable system, which is a semi-polarized integrable system in the sense of Kontsevich and Soibelman. On the Hitchin side, we show that the moduli space of unordered diagonally framed Higgs bundles forms an integrable system in this sense and recovers the meromorphic Hitchin system as the fiberwise compact quotient. Then we construct a new family of quasi-projective Calabi-Yau threefolds and show that its relative intermediate Jacobian fibration, as semi-polarized integrable systems, is isomorphic to the moduli space of unordered diagonally framed Higgs bundles.