Algebraic hyperbolicity of the very general quintic surface in ℙ³

2018/04/11 by Coskun, Izzet, Riedl, Eric
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.04107

Abstract

We prove that a curve of degree dk on a very general surface of degree d ≥ 5 in ℙ³ has geometric genus at least (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 ℙ³ is algebraically hyperbolic.

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