Lorenzo Barban, Geometric Invariant Theory for C*-actions

In this second talk, which is the technical core of the lecture series, we describe several tools to study C*-actions on projective varieties, such as the bandwidth, the AMvsFM Lemma, and the pruning of a variety. With this, we will be able to describe the -birational geometry of the- geometric quotients of a C* action on a pair (X, L), with X a normal projective variety and L an ample line bundle on X. We will conclude by characterizing C*-varieties with small bandwidth.