Folding of Hitchin systems and crepant resolutions

Beck , Florian; Donagi , Ron; Wendland, Katrin

doi:10.1093/imrn/rnaa375

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Folding of Hitchin systems and crepant resolutions

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Wendland, Katrin
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1093/imrn/rnaa375
(Publisher version)

https://doi.org/10.48550/arXiv.2004.04245
(Preprint)

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Citation

Beck, F., Donagi, R., & Wendland, K. (2022). Folding of Hitchin systems and crepant resolutions. International Mathematics Research Notices, 2022(11), 8370-8419. doi:10.1093/imrn/rnaa375.

Cite as: https://hdl.handle.net/21.11116/0000-000A-7FC3-C

Abstract

Folding of ADE-Dynkin diagrams according to graph automorphisms yields
irreducible Dynkin diagrams of ABCDEFG-types. This folding procedure allows to
trace back the properties of the corresponding simple Lie algebras or groups to
those of ADE-type. In this article, we implement the techniques of folding by
graph automorphisms for Hitchin integrable systems. We show that the fixed
point loci of these automorphisms are isomorphic as algebraic integrable
systems to the Hitchin systems of the folded groups away from singular fibers.
The latter Hitchin systems are isomorphic to the intermediate Jacobian
fibrations of Calabi--Yau orbifold stacks constructed by the first author. We
construct simultaneous crepant resolutions of the associated singular
quasi-projective Calabi--Yau threefolds and compare the resulting intermediate
Jacobian fibrations to the corresponding Hitchin systems.