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 $C_{loc}^0(\omega (t))$ topology.

We have to add an additional assumption: the fibres of X over the canonical model X_{can} of X are biholomorphic to each other