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arXiv · 1908.08573

Kobayashi non-hyperbolicity of Calabi-Yau manifolds via mirror symmetry

Ljudmila Kamenova·Cumrun Vafa
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Abstract

A compact complex manifold is Kobayashi non-hyperbolic if there exists an entire curve on it. Using mirror symmetry we establish that there are (possibly singular) elliptic or rational curves on any Calabi-Yau manifold $X$, whose mirror dual $\check X$ exists and is not "Hodge degenerate", therefore proving that $X$ is Kobayashi non-hyperbolic. We are not aware of any higher dimensional simply connected Calabi-Yau manifolds that satisfy the "Hodge degenerate" condition.

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Ljudmila Kamenova, Cumrun Vafa. 2019-08-22. Kobayashi non-hyperbolicity of Calabi-Yau manifolds via mirror symmetry. https://doi.org/10.1007/s00220-020-03719-y

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