The Moser isotopy for holomorphic symplectic and C-symplectic structures
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866914001174134784 |
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| author | Soldatenkov, Andrey Verbitsky, Misha |
| author_facet | Soldatenkov, Andrey Verbitsky, Misha |
| contents | A C-symplectic structure is a complex-valued 2-form which is holomorphically symplectic for an appropriate complex structure. We prove an analogue of Moser's isotopy theorem for families of C-symplectic structures and list several applications of this result. We prove that the degenerate twistorial deformation associated to a holomorphic Lagrangian fibration is locally trivial over the base of this fibration. This is used to extend several theorems about Lagrangian fibrations, known for projective hyperkähler manifolds, to the non-projective case. We also exhibit new examples of non-compact complex manifolds with infinitely many pairwise non-birational algebraic compactifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_00935 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Moser isotopy for holomorphic symplectic and C-symplectic structures Soldatenkov, Andrey Verbitsky, Misha Algebraic Geometry Differential Geometry A C-symplectic structure is a complex-valued 2-form which is holomorphically symplectic for an appropriate complex structure. We prove an analogue of Moser's isotopy theorem for families of C-symplectic structures and list several applications of this result. We prove that the degenerate twistorial deformation associated to a holomorphic Lagrangian fibration is locally trivial over the base of this fibration. This is used to extend several theorems about Lagrangian fibrations, known for projective hyperkähler manifolds, to the non-projective case. We also exhibit new examples of non-compact complex manifolds with infinitely many pairwise non-birational algebraic compactifications. |
| title | The Moser isotopy for holomorphic symplectic and C-symplectic structures |
| topic | Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2109.00935 |