Intermediate Jacobians and ADE Hitchin Systems TeX

@misc{citeulike:771206, 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.}, archivePrefix = {arXiv}, author = {Diaconescu, Duiliu-Emanuel and Donagi, Ron and Pantev, Tony}, citeulike-article-id = {771206}, eprint = {hep-th/0607159}, keywords = {ade, calabi-yau, manifolds, systems}, month = {Jul}, posted-at = {2006-07-24 15:31:56}, priority = {2}, title = {Intermediate Jacobians and ADE Hitchin Systems}, url = {http://arxiv.org/abs/hep-th/0607159}, year = {2006} }

TY - ELEC ID - citeulike:771206 L3 - citeulike-article-id:771206 N2 - 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. TI - Intermediate Jacobians and ADE Hitchin Systems KW - ade KW - calabi-yau KW - manifolds KW - systems AU - Diaconescu, Duiliu-Emanuel AU - Donagi, Ron AU - Pantev, Tony PY - 2006/Jul/21/ UR - http://arxiv.org/abs/hep-th/0607159 ER -