Local inequalities for $cA_k$ singularities
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918132651655168 |
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| author | Krylov, Igor Okada, Takuzo Paemurru, Erik |
| author_facet | Krylov, Igor Okada, Takuzo Paemurru, Erik |
| contents | We generalize an intersection-theoretic local inequality of Fulton-Lazarsfeld to weighted blowups. As a consequence, we obtain the $4n^2/(k+1)$-inequality for isolated $cA_k$ singularities, an analogue of the $4 n^2$-inequality for smooth points. We use this to prove birational rigidity of many families of Fano 3-fold weighted complete intersections with terminal quotient singularities and isolated $cA_k$ singularities, including sextic double solids with $cA_1$ and ordinary $cA_2$ points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21676 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local inequalities for $cA_k$ singularities Krylov, Igor Okada, Takuzo Paemurru, Erik Algebraic Geometry 14J45, 14E08, 14J30, 14C17, 14M10 We generalize an intersection-theoretic local inequality of Fulton-Lazarsfeld to weighted blowups. As a consequence, we obtain the $4n^2/(k+1)$-inequality for isolated $cA_k$ singularities, an analogue of the $4 n^2$-inequality for smooth points. We use this to prove birational rigidity of many families of Fano 3-fold weighted complete intersections with terminal quotient singularities and isolated $cA_k$ singularities, including sextic double solids with $cA_1$ and ordinary $cA_2$ points. |
| title | Local inequalities for $cA_k$ singularities |
| topic | Algebraic Geometry 14J45, 14E08, 14J30, 14C17, 14M10 |
| url | https://arxiv.org/abs/2508.21676 |