摘要： Screw numbers are invariants defined by Nielsen which measure the amount of Dehn twist. For a curve over function field of characteristic 0, we will discuss the relations between some arithmetic heights and screw numbers. For a hyperelliptic curve, we will express its Faltings height as linear combination of screw numbers. For the general case, we will give a universal lower bound for the geometric Bogomolov conjecture , which concerns the finiteness of algebraic points of small height. This is a joint work with Sheng-Li Tan and Jun Lu.