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29 March 2024
 
  » arxiv » 1606.1837

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Higher codimensional Ueda theory for a compact submanifold with unitary flat normal bundle
Takayuki Koike ;
Date 6 Jun 2016
AbstractLet $Y$ 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.
Source arXiv, 1606.1837
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