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Mathematics > Algebraic Geometry

arXiv:1807.05134 (math)
[Submitted on 13 Jul 2018]

Title:Calabi-Yau orbifolds over Hitchin bases

Authors:Florian Beck
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Abstract:Any irreducible Dynkin diagram $\Delta$ is obtained from an irreducible Dynkin diagram $\Delta_h$ of type $\mathrm{ADE}$ by folding via graph automorphisms. For any simple complex Lie group $G$ with Dynkin diagram $\Delta$ and compact Riemann surface $\Sigma$, we give a Lie-theoretic construction of families of quasi-projective Calabi-Yau threefolds together with an action of graph automorphisms over the Hitchin base associated to the pair $(\Sigma, G)$ . These give rise to Calabi-Yau orbifolds over the same base. Their intermediate Jacobian fibration, constructed in terms of equivariant cohomology, is isomorphic to the Hitchin system of the same type away from singular fibers.
Comments: 25 pages. Comments welcome!
Subjects: Algebraic Geometry (math.AG); High Energy Physics - Theory (hep-th)
MSC classes: 14D07 (Primary), 14H70 (Secondary)
Cite as: arXiv:1807.05134 [math.AG]
  (or arXiv:1807.05134v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.05134
Related DOI: https://doi.org/10.1016/j.geomphys.2018.10.010

Submission history

From: Florian Beck [view email]
[v1] Fri, 13 Jul 2018 15:25:38 UTC (34 KB)
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