Hyperbolicity properties of moduli spaces of marked hyperk{ä}hler manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908690794151936 |
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| author | Philippe, Bastien |
| author_facet | Philippe, Bastien |
| contents | We study the hyperbolicity properties of moduli spaces of marked hyperk{ä}hler manifolds along directions corresponding to families having positivity properties for their Hodge bundle. In particular, we show that the Kobayashi pseudo-distance computed using disks tangent to these directions vanishes. As an intermediate step, we establish the existence of families of marked hyperk{ä}hler manifolds over arbitrary curves having a prescribed period map to the corresponding period domain. This generalizes a recent theorem of Greb and Schwald [GS24] to the case of hyperk{ä}hler manifolds of arbitrary dimensions and nonnecessarily compact curves. Finally, using Nevanlinna theory, we establish restrictions on families of hyperk{ä}hler manifolds over C having positive Hodge bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolicity properties of moduli spaces of marked hyperk{ä}hler manifolds Philippe, Bastien Algebraic Geometry Complex Variables We study the hyperbolicity properties of moduli spaces of marked hyperk{ä}hler manifolds along directions corresponding to families having positivity properties for their Hodge bundle. In particular, we show that the Kobayashi pseudo-distance computed using disks tangent to these directions vanishes. As an intermediate step, we establish the existence of families of marked hyperk{ä}hler manifolds over arbitrary curves having a prescribed period map to the corresponding period domain. This generalizes a recent theorem of Greb and Schwald [GS24] to the case of hyperk{ä}hler manifolds of arbitrary dimensions and nonnecessarily compact curves. Finally, using Nevanlinna theory, we establish restrictions on families of hyperk{ä}hler manifolds over C having positive Hodge bundle. |
| title | Hyperbolicity properties of moduli spaces of marked hyperk{ä}hler manifolds |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2512.03638 |