Torsion points on holomorphic sections of elliptic surfaces

A complex algebraic surface is called an elliptic surface if it is a fiber surface whose general fibers are elliptic curves. An elliptic surface can also be regarded as an elliptic curve $E$ over the function field $K$ of an algebraic curve. The holomorphic sections of that elliptic surface can then be regarded as $K$-rational points of $E$. In the 90s, N. Mok proposed and started to use differential geometry to study these $K$-rational points (as holomorphic sections). In this talk, we will discuss how to study the torsions points on such holomorphic sections within this framework. This is based on a joint work with N. Mok.