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arXiv · 2303.12553

Submanifolds with ample normal bundle

Maycol Falla Luza·Frank Loray·Jorge Vitório Pereira
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Abstract

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.

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Maycol Falla Luza, Frank Loray, Jorge Vitório Pereira. 2023-03-22. Submanifolds with ample normal bundle. https://doi.org/10.1112/blms.12955

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