Plane curves, log tangent sheaves and the Geometric Lang-Vojta Conjecture

Eric Riedl, University of Notre Dame

In this talk, we describe two problems relating to plane curves, and describe how log tangent sheaves are key to solving both. First, we consider the natural question: when does the families of lines that intersect with a plane curve vary maximally in modulus? We show how the classical Grauert-Mulich theorem applied to the log tangent sheaf can solve this. Then we consider the question of the algebraic hyperbolicity of the complement of a very general quartic plane curve, and describe how we achieve an answer to this long-open problem, motivated by the Lang-Vojta Conjecture in number theory. This includes joint work with Xi Chen, Anand Patel, Dennis Tseng, and Wern Yeong.

MC 5417