Uniqueness of irreducible desingularization of singularities associated to negative vector bundles
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910603913723904 |
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| author | Deng, Fusheng Li, Yinji Liu, Qunhuan Zhou, Xiangyu |
| author_facet | Deng, Fusheng Li, Yinji Liu, Qunhuan Zhou, Xiangyu |
| contents | We prove that the irreducible desingularization of a singularity given by the Grauert blow down of a negative holomorphic vector bundle over a compact complex manifold is unique up to isomorphism, and as an application, we show that two negative line bundles over compact complex manifolds are isomorphic if and only if their Grauert blow downs have isomorphic germs near the singularities. We also show that there is a unique way to modify a submanifold of a complex manifold to a hypersurface, namely, the blow up of the ambient manifold along the submanifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniqueness of irreducible desingularization of singularities associated to negative vector bundles Deng, Fusheng Li, Yinji Liu, Qunhuan Zhou, Xiangyu Algebraic Geometry Complex Variables We prove that the irreducible desingularization of a singularity given by the Grauert blow down of a negative holomorphic vector bundle over a compact complex manifold is unique up to isomorphism, and as an application, we show that two negative line bundles over compact complex manifolds are isomorphic if and only if their Grauert blow downs have isomorphic germs near the singularities. We also show that there is a unique way to modify a submanifold of a complex manifold to a hypersurface, namely, the blow up of the ambient manifold along the submanifold. |
| title | Uniqueness of irreducible desingularization of singularities associated to negative vector bundles |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2409.09402 |