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- Title
Hitchin and Calabi–Yau integrable systems via variations of Hodge structures.
- Authors
Beck, Florian
- Abstract
Since its discovery by Hitchin in 1987, G -Hitchin systems for a reductive complex Lie group G have extensively been studied. For example, the generic fibers are nowadays well-understood. In this paper, we show that the smooth parts of G -Hitchin systems for a simple adjoint complex Lie group G are isomorphic to non-compact Calabi–Yau integrable systems extending results by Diaconescu–Donagi–Pantev. Moreover, we explain how Langlands duality for Hitchin systems is related to Poincaré–Verdier duality of the corresponding families of quasi-projective Calabi–Yau threefolds. Even though the statement is holomorphic-symplectic, our proof is Hodge-theoretic. It is based on polarizable variations of Hodge structures that admit so-called abstract Seiberg–Witten differentials. These ensure that the associated Jacobian fibration is an algebraic integrable system.
- Subjects
LIE groups
- Publication
Quarterly Journal of Mathematics, 2020, Vol 71, Issue 4, p1345
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/haaa037