On anti-hyperbolicity for hyperkähler varieties
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911252983316480 |
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| author | Kamenova, Ljudmila Lu, Steven |
| author_facet | Kamenova, Ljudmila Lu, Steven |
| contents | By restricting to (a linear subspace of) an affine chart in projective space, a complex stably rational or unirational manifold of dimension $m$ is meromorphically dominable by $\mathbb C^m$, i.e., admits a meromorphic dominating map from $\mathbb C^m$. So are varieties that are birational to abelian varieties and Kummer K3 surfaces. G. Buzzard and the second author have shown that elliptic K3 surfaces are holomorphically dominable by $\mathbb C^2$, i.e. admitting a holomorphic map with nontrivial Jacobian. In this paper we explore various examples and criteria for meromorphic and holomorphic dominability by $\mathbb C^m$ of certain hyperkähler manifolds, generalizing some known results about K3 surfaces. Anti-hyperbolicity has several interpretations in the sense of vanishing of the Kobayashi-Royden metrics, admitting dense entire holomorphic curves, or dominating holomorphic or meromorphic maps from the complex affine space of the same dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On anti-hyperbolicity for hyperkähler varieties Kamenova, Ljudmila Lu, Steven Complex Variables Algebraic Geometry Differential Geometry By restricting to (a linear subspace of) an affine chart in projective space, a complex stably rational or unirational manifold of dimension $m$ is meromorphically dominable by $\mathbb C^m$, i.e., admits a meromorphic dominating map from $\mathbb C^m$. So are varieties that are birational to abelian varieties and Kummer K3 surfaces. G. Buzzard and the second author have shown that elliptic K3 surfaces are holomorphically dominable by $\mathbb C^2$, i.e. admitting a holomorphic map with nontrivial Jacobian. In this paper we explore various examples and criteria for meromorphic and holomorphic dominability by $\mathbb C^m$ of certain hyperkähler manifolds, generalizing some known results about K3 surfaces. Anti-hyperbolicity has several interpretations in the sense of vanishing of the Kobayashi-Royden metrics, admitting dense entire holomorphic curves, or dominating holomorphic or meromorphic maps from the complex affine space of the same dimension. |
| title | On anti-hyperbolicity for hyperkähler varieties |
| topic | Complex Variables Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2511.04714 |