Holomorphic Lagrangian subvarieties in holomorphic symplectic manifolds with Lagrangian fibrations and special Kahler geometry
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866909133973749760 |
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| author | Kamenova, Ljudmila Verbitsky, Misha |
| author_facet | Kamenova, Ljudmila Verbitsky, Misha |
| contents | Let $M$ be a holomorphic symplectic Kähler manifold equipped with a Lagrangian fibration $π$ with compact fibers. The base of this manifold is equipped with a special Kähler structure, that is, a Kähler structure $(I, g, ω)$ and a symplectic flat connection $\nabla$ such that the metric $g$ is locally the Hessian of a function. We prove that any Lagrangian subvariety $Z\subset M$ which intersects smooth fibers of $π$ and smoothly projects to $π(Z)$ is a toric fibration over its image $π(Z)$ in $B$, and this image is also special Kähler. This answers a question of N. Hitchin related to Kapustin-Witten BBB/BAA duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_05497 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Holomorphic Lagrangian subvarieties in holomorphic symplectic manifolds with Lagrangian fibrations and special Kahler geometry Kamenova, Ljudmila Verbitsky, Misha Differential Geometry High Energy Physics - Theory Algebraic Geometry Let $M$ be a holomorphic symplectic Kähler manifold equipped with a Lagrangian fibration $π$ with compact fibers. The base of this manifold is equipped with a special Kähler structure, that is, a Kähler structure $(I, g, ω)$ and a symplectic flat connection $\nabla$ such that the metric $g$ is locally the Hessian of a function. We prove that any Lagrangian subvariety $Z\subset M$ which intersects smooth fibers of $π$ and smoothly projects to $π(Z)$ is a toric fibration over its image $π(Z)$ in $B$, and this image is also special Kähler. This answers a question of N. Hitchin related to Kapustin-Witten BBB/BAA duality. |
| title | Holomorphic Lagrangian subvarieties in holomorphic symplectic manifolds with Lagrangian fibrations and special Kahler geometry |
| topic | Differential Geometry High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/1902.05497 |