Weak transcendental base-point freeness and diameter lower bounds for the K\"ahler-Ricci flow
Junsheng Zhang
TL;DR
This paper establishes a weaker form of transcendental base-point freeness on compact K"ahler manifolds and uses it to derive diameter lower bounds during finite time singularities of the K"ahler-Ricci flow with non-Fano initial data.
Contribution
It introduces a weaker version of transcendental base-point freeness and applies it to analyze diameter bounds in the K"ahler-Ricci flow.
Findings
Proves a weaker transcendental base-point freeness on compact K"ahler manifolds
Derives diameter lower bounds for finite time singularities in K"ahler-Ricci flow
Applies results to non-Fano initial data cases
Abstract
We prove a weaker version of the transcendental base-point freeness on compact K\"ahler manifolds. As a consequence, we derive the diameter lower bound for finite time singularities of K\"ahler-Ricci flow with non-Fano initial data.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory