Infinite-time singularity type of the K\"ahler-Ricci flow

TL;DR

This paper investigates the behavior of the K"ahler-Ricci flow on compact K"ahler manifolds with semi-ample canonical bundles, showing the singularity type at infinity is independent of initial conditions and offering simplified proofs for existing classifications.

Contribution

It proves the independence of the infinite-time singularity type from initial metrics and provides new simplified proofs for classification results.

Findings

Singularity type at infinity is independent of initial metric

Simplified proofs for classification of infinite-time singularities

Enhanced understanding of K"ahler-Ricci flow behavior

Abstract

For the K\"ahler-Ricci flow on a compact K\"ahler manifold with semi-ample canonical line bundle, we prove the singularity type at infinity does not depend on the choice of the initial metric. We also provide new simple proofs for some existing classification results on infinite-time singularity type of the K\"ahler-Ricci flow.