
## 8. Calabi-Yau integrable systems

1. ### Intermediate Jacobian and Hitchin System.

#### Problem 8.1.

Give a geometric description of how the intermediate Jacobian systems of [MR2350120] and [arXiv:1707.05973] are related to the Hitchin system.
A resolution to this problem might answer the question: Given a point in the intermediate Jacobian, how do you construct a Higgs bundle? The isomorphisms given in the papers referenced above apparently arise non-explicitly via the Leray spectral sequence from the Calabi-Yau’s to the curve.
• #### Problem 8.2.

Given a non-compact Calabi-Yau integrable system, recognize whether it is a Nakajima quiver variety.

Cite this as: AimPL: Singular geometry and Higgs bundles in string theory, available at http://aimpl.org/singularhiggs.