| Résume | Searching for canonical metrics in Kähler classes has been a central theme in Kähler geometry for decades. This talk aims to explain a method for studying singular canonical metrics in families of singular varieties with a relative pluripotential theory and a variational approach in families. The main focus of the talk will be the singular Kähler-Einstein (KE) metrics on families of Fano varieties. Following a brief review of singular KE metrics and a variational method, I will introduce a notion of convergence of quasi-plurisubharmonic functions in families. Several classical properties will be extended under this framework. Then, I will present an Euclidien openness result of the existence of KE metrics via an analytic method and how to establish uniform a priori estimates in families. If time permits, we will conclude by exploring the potential development of this method to study singular cscK metrics. |
