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HIGHER CODIMENSIONAL UEDA THEORY FOR A COMPACT SUBMANIFOLD WITH UNITARY FLAT NORMAL BUNDLE

Part of: Cycles and subschemes Compact analytic spaces

Published online by Cambridge University Press:  13 June 2018

TAKAYUKI KOIKE
TAKAYUKI KOIKE*
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan email tkoike@sci.osaka-cu.ac.jp
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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 nonsingular 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 semipositive curvature on a nef line bundle.

MSC classification

Primary: 32J25: Transcendental methods of algebraic geometry 14C20: Divisors, linear systems, invertible sheaves
Type
Article
Information
Nagoya Mathematical Journal , Volume 238 , June 2020 , pp. 104 - 136
Copyright
© 2018 Foundation Nagoya Mathematical Journal

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