Speaker: 

Lei Ni

Institution: 

UC San Diego

Time: 

Tuesday, May 31, 2022 - 4:00pm

Location: 

ISEB 1200

A joint Geometry and Analysis seminar.

 

Abstract: The k-Ricci curvature interpolates between the Ricci curvature and holomorphic sectional curvature. For the positive case, a recent result asserts that the compact Kaehler manifolds with positive k-Ricci are  projective and rationally connected. This generalizes the previous results of Campana, Kollar-Miyaoka-Mori for the Fano case and the Heirer-Wong and Yang for holomorphic sectional curvature case. For the negative case, all compact Kaehler manifolds with negative k-Ricci admit a Kaehler-Einstein metric with negative scalar curvature. I shall explain how to get this result by solving a complex Monge-Ampere equation.