Shengli Tan, East China Normal University, Shanghai

Global and local Chern numbers of families of algebraic curves and applications

Abstract

We will talk about some problems on the global and local Chern numbers of families of algebraic curves. As applications, we will construct families of hyperelliptic curves with the highest slopes, classify some families of curves over P¹ with 3 singular fibers and present optimal upper bounds on the abelian automorphism groups of surfaces of general type. This is a survey of some recent joint work with C. Gong, J. Lu, X. Lv, X.-L. Liu, F. Yu, K. Zuo.