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- Title
Folding of Hitchin Systems and Crepant Resolutions.
- Authors
Beck, Florian; Donagi, Ron; Wendland, Katrin
- Abstract
Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of |$\textrm{ABCDEFG}$| -types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of |$\textrm{ADE}$| -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 1st author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi–Yau three-folds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems.
- Subjects
DYNKIN diagrams; GROUP algebras; LIE algebras; LIE groups; JACOBIAN matrices
- Publication
IMRN: International Mathematics Research Notices, 2022, Vol 2022, Issue 11, p8370
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnaa375