Non-hyperbolicity of holomorphic symplectic varieties
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866917534538661888 |
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| author | Kamenova, Ljudmila Lehn, Christian |
| author_facet | Kamenova, Ljudmila Lehn, Christian |
| contents | We prove non-hyperbolicity of primitive symplectic varieties with $b_2 \geq 5$ that satisfy the rational SYZ conjecture. If in addition $b_2 \geq 7$, we establish that the Kobayashi pseudometric vanishes identically. This in particular applies to all currently known examples of irreducible symplectic manifolds and thereby completes the results by Kamenova--Lu--Verbitsky. The key new contribution is that a projective primitive symplectic variety with a Lagrangian fibration has vanishing Kobayashi pseudometric. The proof uses ergodicity, birational contractions, and cycle spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11411 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-hyperbolicity of holomorphic symplectic varieties Kamenova, Ljudmila Lehn, Christian Algebraic Geometry Complex Variables Differential Geometry 32Q45, 53C26 (Primary), 14B07, 14J10, 32S45 (Secondary) We prove non-hyperbolicity of primitive symplectic varieties with $b_2 \geq 5$ that satisfy the rational SYZ conjecture. If in addition $b_2 \geq 7$, we establish that the Kobayashi pseudometric vanishes identically. This in particular applies to all currently known examples of irreducible symplectic manifolds and thereby completes the results by Kamenova--Lu--Verbitsky. The key new contribution is that a projective primitive symplectic variety with a Lagrangian fibration has vanishing Kobayashi pseudometric. The proof uses ergodicity, birational contractions, and cycle spaces. |
| title | Non-hyperbolicity of holomorphic symplectic varieties |
| topic | Algebraic Geometry Complex Variables Differential Geometry 32Q45, 53C26 (Primary), 14B07, 14J10, 32S45 (Secondary) |
| url | https://arxiv.org/abs/2212.11411 |