Year: 2025
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Kamenova, Ljudmila, Lu, Steven
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7104632999
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