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arXiv · 2504.10790

Ahlfors Currents and Symplectic Non-Hyperbolicity

Spencer Cattalani
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Abstract

Complex (affine) lines are a major object of study in complex geometry, but their symplectic aspects are not well understood. Inspired by Duval's work on Ahlfors currents, we use them to perform a systematic study of complex lines in symplectic manifolds. In particular, we generalize (by a different method and under topological assumptions) a result of Bangert on the existence of complex lines. We show that Ahlfors currents control the asymptotic behavior of families of pseudoholomorphic curves, refining a result of Demailly. Lastly, we show that the space of Ahlfors currents is convex.

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Spencer Cattalani. 2025-04-15. Ahlfors Currents and Symplectic Non-Hyperbolicity. https://arxiv.org/abs/2504.10790

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