Intermediate Jacobians and ADE Hitchin Systems
| dc.creator | Diaconescu, Duiliu-Emanuel | |
| dc.creator | Donagi, Ron | |
| dc.creator | Pantev, Tony | |
| dc.date | 2006-07-21 | |
| dc.date | 2006-07-24 | |
| dc.date.accessioned | 2026-07-07T07:16:52Z | |
| dc.date.available | 2026-07-07T07:16:52Z | |
| dc.description | Let $Σ$ 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 $(Σ, \mathfrak{g})$, we construct a family of quasi-projective Calabi-Yau threefolds parameterized by the base of the Hitchin integrable system associated to $(Σ,\mathfrak{g})$. 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. | |
| dc.description | 14 pages, LaTeX2e, typos fixed, acknowledgments added | |
| dc.identifier | https://arxiv.org/abs/hep-th/0607159 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0607159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113743 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Intermediate Jacobians and ADE Hitchin Systems | |
| dc.type | text |