Independence of Singularity Type for Numerically Effective K\"ahler-Ricci Flows

TL;DR

This paper proves that the singularity type of solutions to the K"ahler-Ricci flow on a numerically effective manifold is independent of the initial metric, extending previous results to a broader class of manifolds.

Contribution

It establishes the invariance of singularity type for K"ahler-Ricci flows on numerically effective manifolds, generalizing earlier work by Y. Zhang.

Findings

Singularity type remains constant regardless of initial metric.

Type III solutions imply all solutions are Type III.

Generalizes previous semi-ample case results.

Abstract

In this paper, we show that the singularity type of solutions to the K\"aher-Ricci flow on a numerically effective manifold does not depend on the initial metric. More precisely if there exists a type III solution to the K\"ahler-Ricci flow, then any other solution starting from a different initial metric will also be Type III. This generalises previous results by Y. Zhang for the semi-ample case.