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arXiv · 1606.01837

Higher codimensional Ueda theory for a compact submanifold with unitary flat normal bundle

Takayuki Koike
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Abstract

Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. Our interest is in a sort of the linearizability problem of a neighborhood of $Y$. As a higher-codimensional generalization of Ueda's result, we give a sufficient condition for the existence of a non-singular holomorphic foliation on a neighborhood of $Y$ which includes $Y$ as a leaf with unitary-linear holonomy. We apply this result to the existence problem of a smooth Hermitian metric with semi-positive curvature on a nef line bundle.

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Takayuki Koike. 2016-06-06. Higher codimensional Ueda theory for a compact submanifold with unitary flat normal bundle. https://arxiv.org/abs/1606.01837

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