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8. Calabi-Yau integrable systems

    1. Intermediate Jacobian and Hitchin System.


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      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.


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          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.