On transversely holomorphic foliations with homogeneous transverse structure

Q3 Mathematics
Liliana Jurado, Bruno Scardua
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引用次数: 0

Abstract

In this paper we study transversely holomorphic foliations of complex codimension one with a transversely homogeneous complex transverse structure. We prove that the only cases are the transversely additive, affine and projective cases. We shall focus on the transversely affine case and describe the holonomy of a leaf which is "at the infinity" with respect to this structure and prove this is a solvable group. Using this we are able to prove linearization results for the foliation under the assumption of existence of some hyperbolic map in the holonomy group. Such foliations will then be given by simple-poles closed transversely meromorphic one-forms.
关于具有均匀横向结构的横向全纯叶理
本文研究了具有横向齐次复横向结构的复余维为1的横向全纯叶理。我们证明了只有横向加性、仿射性和射影性的情况。我们将着重于横向仿射的情况,描述一个叶的“在无穷远处”的完整性,并证明它是一个可解群。在完整群中存在双曲映射的假设下,证明了叶理的线性化结果。这样的叶将由单极闭合横向亚纯单形给出。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Proceedings of the International Geometry Center
Proceedings of the International Geometry Center Mathematics-Geometry and Topology
CiteScore
1.00
自引率
0.00%
发文量
14
审稿时长
3 weeks
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