Kähler-Einstein metrics on families of Fano varieties

04/03/2023 10:00 am - 11:00 am
Charles Doran Mauricio Romo Tsung-Ju Lee
CMSA Room G02
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Algebraic Geometry in String Theory Seminar

Speaker: Chung-Ming Pan, Institut de Mathématiques de Toulouse

Title: Kähler-Einstein metrics on families of Fano varieties

Abstract: This talk aims to introduce a pluripotential approach to study uniform a priori estimates of Kähler-Einstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory and the variational approach to complex Monge-Ampère equations. I will then define a notion of convergence of quasi-plurisubharmonic functions in families of normal varieties and extend several classical properties under this context. Last, I will explain how these elements help to obtain a purely analytic proof of the openness of existing singular KE metrics and a uniform $L^\infty$ estimate of KE potentials. This is joint work with Antonio Trusiani.