On the Ricci curvature of Kahler-Ricci Flow

Abstract

In this paper, we consider $n$-dimensional compact K$\ddot{a}$hler manifold with semi-ample canonical line bundle under the long time solution of K$\ddot{a}$hler Ricci Flow. In particular, if the Kodaira dimension is one, Ricci curvature converge to negative of generalized K$\ddot{a}$hler Einstein metric $\omega_B$ locally away from singular set in $C^0_{loc}(\omega(t))$ topology.