Examples of non-trivial rank in locally conformal Kähler geometry

被引:0
|
作者
Maurizio Parton
Victor Vuletescu
机构
[1] Università di Chieti-Pescara,Dipartimento di Scienze
[2] University of Bucharest,Faculty of Mathematics and Informatics
来源
Mathematische Zeitschrift | 2012年 / 270卷
关键词
Complex Manifold; Galois Group; Betti Number; Maximal Rank; Galois Extension;
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学科分类号
摘要
We consider locally conformal Kähler geometry as an equivariant, homothetic Kähler geometry (K, Γ). We show that the de Rham class of the Lee form can be naturally identified with the homomorphism projecting Γ to its dilation factors, thus completing the description of locally conformal Kähler geometry in this equivariant setting. The rank rM of a locally conformal Kähler manifold is the rank of the image of this homomorphism. Using algebraic number theory, we show that rM is non-trivial, providing explicit examples of locally conformal Kähler manifolds with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${1\nless{\text{\upshape \rmfamily r}_{M}}\nless b_1}$$\end{document}. As far as we know, these are the first examples of this kind. Moreover, we prove that locally conformal Kähler Oeljeklaus-Toma manifolds have either rM = b1 or rM = b1/2.
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页码:179 / 187
页数:8
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