On the exceptional set of crepant resolutions of abelian singularities
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915251282247680 |
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| author | Bruzzo, Ugo Ferreira, Fábio Arceu |
| author_facet | Bruzzo, Ugo Ferreira, Fábio Arceu |
| contents | Let G be a finite abelian subgroup of SL(n,C), and suppose there exists a toric crepant resolution phi: X -- > C^n/G. We prove that for each component E of the exceptional set of phi there exists an open subset U of X that contains E and is isomorphic to the total space of the canonical bundle of E. This contributes to the collection of results aimed at solving a classical problem, i.e., to determine which submanifolds of a complex manifold have a neighborhood isomorphic to a neighborhood of the zero section of their normal bundle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_06810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the exceptional set of crepant resolutions of abelian singularities Bruzzo, Ugo Ferreira, Fábio Arceu Algebraic Geometry 14E15, 14B05, 14J27, 14M25 Let G be a finite abelian subgroup of SL(n,C), and suppose there exists a toric crepant resolution phi: X -- > C^n/G. We prove that for each component E of the exceptional set of phi there exists an open subset U of X that contains E and is isomorphic to the total space of the canonical bundle of E. This contributes to the collection of results aimed at solving a classical problem, i.e., to determine which submanifolds of a complex manifold have a neighborhood isomorphic to a neighborhood of the zero section of their normal bundle. |
| title | On the exceptional set of crepant resolutions of abelian singularities |
| topic | Algebraic Geometry 14E15, 14B05, 14J27, 14M25 |
| url | https://arxiv.org/abs/2504.06810 |