Singular Kähler--Ricci shrinkers and polarized Fano fibrations

Abstract

We prove that any singular Kähler--Ricci shrinker $X$ arising as a noncollapsed limit of Kähler--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 Kähler--Ricci flows.

arXiv comment63 pages. v2: Title changed and a new section added to strengthen our previous results. Comments welcome!