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- W1505265349 abstract "Let $Sigma$ be a smooth projective complex curve and $mathfrak{g}$ a simple Lie algebra of type ${sf ADE}$ with associated adjoint group $G$. For a fixed pair $(Sigma, mathfrak{g})$, we construct a family of quasi-projective Calabi-Yau threefolds parameterized by the base of the Hitchin integrable system associated to $(Sigma,mathfrak{g})$. Our main result establishes an isomorphism between the Calabi-Yau integrable system, whose fibers are the intermediate Jacobians of this family of Calabi-Yau threefolds, and the Hitchin system for $G$, whose fibers are Prym varieties of the corresponding spectral covers. This construction provides a geometric framework for Dijkgraaf-Vafa transitions of type ${sf ADE}$. In particular, it predicts an interesting connection between adjoint ${sf ADE}$ Hitchin systems and quantization of holomorphic branes on Calabi-Yau manifolds." @default.
- W1505265349 created "2016-06-24" @default.
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- W1505265349 date "2006-07-21" @default.
- W1505265349 modified "2023-09-27" @default.
- W1505265349 title "Intermediate Jacobians and ADE Hitchin Systems" @default.
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