KASS seminar

Abstract: The study of constant scalar curvature Kähler (cscK) metrics on compact complex manifolds is a classical topic that has attracted enormous interest since the 1950s. However, detecting the existence of cscK metrics is a difficult task, which in the projective case conjecturally amounts to proving an important algebro-geometric stability notion.

In 2006, Arezzo and Pacard showed that having cscK metrics is a property that is preserved by blowing-up distint points on compact Kähler manifolds with discrete automorphism groups. This result has been recently extended by Seyyedali and Székélyhidi to blow-ups along submanifolds. In the talk, I will present a further "optimal" generalization that replaces blow-ups along submanifolds with modifications (holomorphic bimeromorphic maps). The proof only uses pluripotential-theoretical techniques and it can be very likely adapted to other situations. Time permitting, in the last part of the talk I will discuss applications and future developments.