Submanifolds with ample normal bundle
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911789370834944 |
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| author | Luza, Maycol Falla Loray, Frank Pereira, Jorge Vitório |
| author_facet | Luza, Maycol Falla Loray, Frank Pereira, Jorge Vitório |
| contents | We construct germs of complex manifolds of dimension $m$ along projective submanifolds of dimension $n$ with ample normal bundle and without non-constant meromorphic functions whenever $m \geq 2n$. We also show that our methods do not allow the construction of similar examples when $m < 2n$ by establishing an algebraicity criterion for foliations on projective spaces which generalizes a classical result by Van den Ven characterizing linear subspaces of projective spaces as the only submanifolds with split tangent sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_12553 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Submanifolds with ample normal bundle Luza, Maycol Falla Loray, Frank Pereira, Jorge Vitório Algebraic Geometry Complex Variables 51M15, 32S65 We construct germs of complex manifolds of dimension $m$ along projective submanifolds of dimension $n$ with ample normal bundle and without non-constant meromorphic functions whenever $m \geq 2n$. We also show that our methods do not allow the construction of similar examples when $m < 2n$ by establishing an algebraicity criterion for foliations on projective spaces which generalizes a classical result by Van den Ven characterizing linear subspaces of projective spaces as the only submanifolds with split tangent sequence. |
| title | Submanifolds with ample normal bundle |
| topic | Algebraic Geometry Complex Variables 51M15, 32S65 |
| url | https://arxiv.org/abs/2303.12553 |