Hermitian-symplectic and Kahler structures on degenerate twistor deformations
| Autor: | Soldatenkov, Andrey, Verbitsky, Misha |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Let $(M, \Omega)$ be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration $\pi: M \to B$, and $\eta$ a closed $(1,1)$-form on $B$. Then $\Omega+ \pi^* \eta$ is a holomorphically symplectic form on a complex manifold which is called the degenerate twistor deformation of $M$. We prove that degenerate twistor deformations of compact holomorphically symplectic K\"ahler manifolds are also K\"ahler. First, we prove that degenerate twistor deformations are Hermitian symplectic, that is, tamed by a symplectic form; this is shown using positive currents and an argument based on the Hahn--Banach theorem, originally due to Sullivan. Then we apply a version of Huybrechts's theorem showing that two non-separated points in the Teichm\"uller space of holomorphically symplectic manifolds correspond to bimeromorphic manifolds if they are Hermitian symplectic. Comment: 24 pages, v. 1.0 |
| Databáze: | arXiv |
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