On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866910558089904128 |
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| author | Li, Yang Tosatti, Valentino |
| author_facet | Li, Yang Tosatti, Valentino |
| contents | We study the collapsing of Calabi-Yau metrics and of Kahler-Ricci flows on fiber spaces where the base is smooth. We identify the collapsed Gromov-Hausdorff limit of the Kahler-Ricci flow when the divisorial part of the discriminant locus has simple normal crossings. In either setting, we also obtain an explicit bound for the real codimension 2 Hausdorff measure of the Cheeger-Colding singular set, and identify a sufficient condition from birational geometry to understand the metric behavior of the limiting metric on the base. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_00836 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows Li, Yang Tosatti, Valentino Differential Geometry Algebraic Geometry Metric Geometry 32Q25, 32Q20, 32W20, 14J32, 53C25 We study the collapsing of Calabi-Yau metrics and of Kahler-Ricci flows on fiber spaces where the base is smooth. We identify the collapsed Gromov-Hausdorff limit of the Kahler-Ricci flow when the divisorial part of the discriminant locus has simple normal crossings. In either setting, we also obtain an explicit bound for the real codimension 2 Hausdorff measure of the Cheeger-Colding singular set, and identify a sufficient condition from birational geometry to understand the metric behavior of the limiting metric on the base. |
| title | On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows |
| topic | Differential Geometry Algebraic Geometry Metric Geometry 32Q25, 32Q20, 32W20, 14J32, 53C25 |
| url | https://arxiv.org/abs/2107.00836 |