Rigidity of Lagrangian embeddings into symplectic tori and K3 surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916254808276992 |
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| author | Entov, Michael Verbitsky, Misha |
| author_facet | Entov, Michael Verbitsky, Misha |
| contents | A Kahler-type form is a symplectic form compatible with an integrable complex structure. Let M be either a torus or a K3-surface equipped with a Kahler-type form. We show that the homology class of any Maslov-zero Lagrangian torus in M has to be non-zero and primitive. This extends previous results of Abouzaid-Smith (for tori) and Sheridan-Smith (for K3-surfaces) who proved it for particular Kahler-type forms on M. In the K3 case our proof uses dynamical properties of the action of the diffeomorphism group of M on the space of the Kahler-type forms. These properties are obtained using Shah's arithmetic version of Ratner's orbit closure theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_05971 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Rigidity of Lagrangian embeddings into symplectic tori and K3 surfaces Entov, Michael Verbitsky, Misha Symplectic Geometry 57R17, 53D12, 53C26, 32Q15 A Kahler-type form is a symplectic form compatible with an integrable complex structure. Let M be either a torus or a K3-surface equipped with a Kahler-type form. We show that the homology class of any Maslov-zero Lagrangian torus in M has to be non-zero and primitive. This extends previous results of Abouzaid-Smith (for tori) and Sheridan-Smith (for K3-surfaces) who proved it for particular Kahler-type forms on M. In the K3 case our proof uses dynamical properties of the action of the diffeomorphism group of M on the space of the Kahler-type forms. These properties are obtained using Shah's arithmetic version of Ratner's orbit closure theorem. |
| title | Rigidity of Lagrangian embeddings into symplectic tori and K3 surfaces |
| topic | Symplectic Geometry 57R17, 53D12, 53C26, 32Q15 |
| url | https://arxiv.org/abs/2105.05971 |