Singular Kähler-Ricci Shrinkers are Complex Analytic
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916044399968256 |
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| author | Hallgren, Max Zhang, Junsheng |
| author_facet | Hallgren, Max Zhang, Junsheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25213 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singular Kähler-Ricci Shrinkers are Complex Analytic Hallgren, Max Zhang, Junsheng Differential Geometry Complex Variables 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. |
| title | Singular Kähler-Ricci Shrinkers are Complex Analytic |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2605.25213 |