Optimal bounds for local volumes of threefold singularities
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912751024078848 |
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| author | Liu, Yuchen |
| author_facet | Liu, Yuchen |
| contents | We establish an optimal upper bound for local volumes of Gorenstein canonical non-hypersurface threefold singularities. Specifically, we show that a klt threefold singularity with local volume at least $9$ is either a hypersurface singularity or a quotient singularity. As applications, we obtain new restrictions on the singularities of members in K-moduli spaces of Fano threefolds, and we establish a sharp inequality between local volumes and minimal log discrepancies for threefold singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05429 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal bounds for local volumes of threefold singularities Liu, Yuchen Algebraic Geometry Commutative Algebra Differential Geometry We establish an optimal upper bound for local volumes of Gorenstein canonical non-hypersurface threefold singularities. Specifically, we show that a klt threefold singularity with local volume at least $9$ is either a hypersurface singularity or a quotient singularity. As applications, we obtain new restrictions on the singularities of members in K-moduli spaces of Fano threefolds, and we establish a sharp inequality between local volumes and minimal log discrepancies for threefold singularities. |
| title | Optimal bounds for local volumes of threefold singularities |
| topic | Algebraic Geometry Commutative Algebra Differential Geometry |
| url | https://arxiv.org/abs/2512.05429 |