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 locally algebraic complex-analytic variety with log terminal singularities. We then derive several geometric consequences: $X$ is simply connected, has a unique end, has unique tangent cones at every point, and is a smooth orbifold outside a subset of complex codimension at least three. As a further application, we prove a new long-time pseudolocality theorem for almost-selfsimilar Kähler--Ricci flows.
| Comments: | 47 pages. Comments welcome! |
| Subjects: | Differential Geometry (math.DG); Complex Variables (math.CV) |
| Cite as: | arXiv:2605.25213 [math.DG] |
| (or arXiv:2605.25213v1 [math.DG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25213 arXiv-issued DOI via DataCite (pending registration) |
From: Max Hallgren [view email]
[v1]
Sun, 24 May 2026 18:30:41 UTC (63 KB)
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