HIGHER CODIMENSIONAL UEDA THEORY FOR A COMPACT SUBMANIFOLD WITH UNITARY FLAT NORMAL BUNDLE
HIGHER CODIMENSIONAL UEDA THEORY FOR A COMPACT SUBMANIFOLD WITH UNITARY FLAT NORMAL BUNDLE
复制标题
酉平法束紧致子流形的高维UEDA理论
作者：
T. Koike
设Y是一个紧复流形，它嵌入到一个具有酉平坦法丛的复流形中.我们感兴趣的是一种线性化问题的邻域$Y$。作为上田结果的高余维推广，我们给出了一个非奇异全纯叶理存在于Y的邻域上的充分条件，该邻域包含Y作为酉线性完整的叶。我们将这个结果应用到Nef线丛上具有半正曲率的光滑Hermitian度量的存在性问题。
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.