Topics on rationally connected varieties

Abstract

In this thesis we study different questions on rationally connected varieties. The first and second part are devoted to the studies of degenerations of rationally connected varieties over an arbitrary field of characteristic zero and the finite fields. In the third part, we study the finite groups that are the fundamental groups of smooth loci of log del Pezzo surfaces. A short table containing these groups is given. Many of groups on the table are proved to be fundamental groups.