Convergence of scalar curvature of Kahler-Ricci flow on manifolds of positive Kodaira dimension

Abstract

In this paper, we consider Kahler-Ricci flow on n-dimensional Kahler manifold with semi-ample canonical line bundle and 0< m:= Kod(X)<n. Such manifolds admit a Calabi-Yau fibration over its canonical model. We prove that the scalar curvature of the Kahler metric along the normalized Kahler-Ricci flow converge to -m outside the singular set of this fibration.

arXiv comment23 pages. All comments are welcome

References in corpus (1)

• A remark on constant scalar curvature Kähler metrics on minimal models

Cited by in corpus (5)

• Local curvature estimates of long-time solutions to the Kähler-Ricci flow
• A "boundedness implies convergence" principle and its applications to collapsing estimates in Kähler geometry
• Diameter and Ricci curvature estimates for long-time solutions of the Kahler-Ricci flow
• A remark on constant scalar curvature Kähler metrics on minimal models
• Global higher order estimates for collapsing Calabi-Yau metrics on elliptic K3 surfaces