Algebraic hyperbolicity of the very general quintic surface in P^3.
Algebraic hyperbolicity of the very general quintic surface in P^3.
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P^3 中非常一般的五次曲面的代数双曲性。
DOI：
10.1016/j.aim.2019.04.062
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发表时间：
2019
影响因子：
1.7
通讯作者：
Riedl, Eric
中科院分区：
文献类型：
--
作者：
Coskun, Izzet;Riedl, Eric
我们证明了在P3中一个非常一般的d≥ 5次曲面上的dk次曲线的几何亏格至少为dk（d− 5）+k2 + 1.这是对耿旭著名的属界的重大改进。作为推论，我们推导出一个非常一般的五次曲面在P 3的代数双曲，解决了一个长期存在的猜想Demailly。这完全决定了P3中哪些非常一般的超曲面是代数双曲的。
We prove that a curve of degree dk on a very general surface of degree d≥ 5 in P 3 has geometric genus at least d k (d− 5)+ k 2+ 1. This gives a substantial improvement on the celebrated genus bounds of Geng Xu. As a corollary, we deduce the algebraic hyperbolicity of a very general quintic surface in P 3, resolving a long-standing conjecture of Demailly. This completely determines which very general hypersurfaces in P 3 are algebraically hyperbolic.