Upper bound on the multiplicity of rational and Du Bois singularities
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912650859905024 |
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| author | Park, Sung Gi |
| author_facet | Park, Sung Gi |
| contents | This paper resolves a question of Huneke and Watanabe by proving a sharp upper bound for the multiplicity of Du Bois singularities: at a point of a $d$-dimensional variety with Du Bois singularities and embedding dimension $e$, the multiplicity is at most $\binom{e}{d}$. Additionally, the result recovers the previously known upper bound for the multiplicity of rational singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Upper bound on the multiplicity of rational and Du Bois singularities Park, Sung Gi Algebraic Geometry 13H15, 14B05 This paper resolves a question of Huneke and Watanabe by proving a sharp upper bound for the multiplicity of Du Bois singularities: at a point of a $d$-dimensional variety with Du Bois singularities and embedding dimension $e$, the multiplicity is at most $\binom{e}{d}$. Additionally, the result recovers the previously known upper bound for the multiplicity of rational singularities. |
| title | Upper bound on the multiplicity of rational and Du Bois singularities |
| topic | Algebraic Geometry 13H15, 14B05 |
| url | https://arxiv.org/abs/2509.21807 |