The cone theorem for Kahler varieties
Organizers
Speaker
Christopher Derek Hacon
Time
Thursday, March 6, 2025 10:00 AM - 11:00 AM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
The cone theorem is a cornestone of higher dimensional birational geometry for complex projective varieties $X\subset P^N_C$. Roughly speaking it says that the failure of positivity of the canonical line bundle $\omega _X$ of a complex projective manifold $X$ is explained by the existence of rational curves that intersect the canonical line bundle negatively $c_1(\omega _X)\cdot C < 0$. In this talk we will show that the cone theorem also holds for Kahler varieties with mild singularities. In particular if $X$ is a Kahler manifold containing no rational curves, then $\omega _X$ is nef.