Xi Chen

It is conjectured that there are infinitely many rational curves on every projective K3 surface. A large part of this conjecture was proved by Jun Li and Christian Liedtke, based on the characteristic p reduction method proposed by Bogomolov-Hassett...

It is expected that a general K3 surface does not admit self rational maps of degree > 1. I'll give a proof of this conjecture for K3 surfaces of genus at least 4.