In this lecture series we aim to describe the rich relation between C*-actions on complex normal projetive varieties and the birational maps among the associated geometric quotients. We will begin this first seminar by explaining a motivating example, called the Atiyah flop. We will then discuss general results on normal projective varieties admitting a C*-action, such as Sumihiro’s theorem and Białynicki-Birula theorem. We will then conclude by describing how much a C*-action affects the birational geometry of a C*-variety.
