In this talk we focus on complex, smooth, projective varieties  admitting a non-trivial C*-action. We introduce a new approach to investigate such varieties, using instruments coming from birational geometry. In particular, we relate small bandwidth varieties with Atiyah flips and special Cremona transformations. We report recent classification results of small bandwidth varieties, with particular  attention to the case of bandwidth 3. We finally discuss some  applications, in the framework of LeBrun-Salamon conjecture. This is a  joint project with G. Occhetta, L. Solá Conde and J. Wiśniewski.

 

The seminar will take place online. Click here for the Zoom link.