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July, 2017 Absolutely $k$-convex domains and holomorphic foliations on homogeneous manifolds
Maurício CORRÊA Jr., Arturo FERNÁNDEZ-PÉREZ
J. Math. Soc. Japan 69(3): 1235-1246 (July, 2017). DOI: 10.2969/jmsj/06931235

Abstract

We consider a holomorphic foliation $\mathcal{F}$ of codimension $k\geq 1$ on a homogeneous compact Kähler manifold $X$ of dimension $n \gt k$. Assuming that the singular set ${\rm Sing}(\mathcal{F})$ of $\mathcal{F}$ is contained in an absolutely $k$-convex domain $U\subset X$, we prove that the determinant of normal bundle $\det(N_{\mathcal{F}})$ of $\mathcal{F}$ cannot be an ample line bundle, provided $[n/k]\geq 2k+3$. Here $[n/k]$ denotes the largest integer $\leq n/k.$

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Maurício CORRÊA Jr.. Arturo FERNÁNDEZ-PÉREZ. "Absolutely $k$-convex domains and holomorphic foliations on homogeneous manifolds." J. Math. Soc. Japan 69 (3) 1235 - 1246, July, 2017. https://doi.org/10.2969/jmsj/06931235

Information

Published: July, 2017
First available in Project Euclid: 12 July 2017

zbMATH: 06786996
MathSciNet: MR3685043
Digital Object Identifier: 10.2969/jmsj/06931235

Subjects:
Primary: 32S65
Secondary: 32F10

Rights: Copyright © 2017 Mathematical Society of Japan

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Vol.69 • No. 3 • July, 2017
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