2017/02/02 by Dohyeong Kim, Kim, Dohyeong
Mathematics · #Algebraic Geometry and Number Theory #Mathematics and Applications #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.1702.00735
Let Y be the complement of a plane quartic curve D defined over a number field. Our main theorem confirms the Lang-Vojta conjecture for Y when D is a generic smooth quartic curve, by showing that its integral points are confined in a curve except for a finite number of exceptions. The required finiteness will be obtained by reducing it to the Shafarevich conjecture for K3 surfaces. Some variants of our method confirm the same conjecture when D is a reducible generic quartic curve which consists of four lines, two lines and a conic, or two conics.