Singular K\"ahler--Ricci shrinkers and polarized Fano fibrations

Max Hallgren; Junsheng Zhang

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arXiv · 2605.25213

Singular K\"ahler--Ricci shrinkers and polarized Fano fibrations

Max Hallgren·Junsheng Zhang

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Abstract

We prove that any singular K\"ahler--Ricci shrinker $X$ arising as a noncollapsed limit of K\"ahler--Ricci flows admits a natural structure of a polarized Fano fibration. We also show that it is simply connected, has unique tangent cones at every point, and is a smooth orbifold outside a subset of complex codimension at least three. As an application, we prove a new long-time pseudolocality theorem for almost-selfsimilar K\"ahler--Ricci flows.

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Max Hallgren, Junsheng Zhang. 2026-05-24. Singular K\"ahler--Ricci shrinkers and polarized Fano fibrations. https://arxiv.org/abs/2605.25213

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