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arXiv · 1804.04107

Algebraic hyperbolicity of the very general quintic surface in $\mathbb{P}^3$

Izzet Coskun·Eric Riedl
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Abstract

We prove that a curve of degree $dk$ on a very general surface of degree $d \geq 5$ in $\mathbb{P}^3$ has geometric genus at least $\frac{dk(d-5)+k}{2} + 1$. This improves bounds given by G. Xu. As a corollary, we conclude that the very general quintic surface in $\mathbb{P}^3$ is algebraically hyperbolic.

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Izzet Coskun, Eric Riedl. 2018-04-11. Algebraic hyperbolicity of the very general quintic surface in $\mathbb{P}^3$. https://arxiv.org/abs/1804.04107

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