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Singular Kähler--Ricci shrinkers and polarized Fano fibrations

  • Max Hallgren
  • Junsheng Zhang
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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.

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Cite

BibTeXRIS
BibTeX
@misc{hallgren2026singular,
  title = {{Singular Kähler--Ricci shrinkers and polarized Fano fibrations}},
  author = {Max Hallgren and Junsheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2605.25213},
  eprint = {2605.25213},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.25213},
}
RIS
TY  - UNPB
TI  - Singular Kähler--Ricci shrinkers and polarized Fano fibrations
AU  - Max Hallgren
AU  - Junsheng Zhang
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2605.25213
UR  - https://arxiv.org/abs/2605.25213
AB  - 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.
ER  -