A -TYPE CONDITION BEYOND THE KÄHLER REALM

IF 1.1 2区数学 Q1 MATHEMATICS

Journal of the Institute of Mathematics of Jussieu Pub Date : 2023-11-28 DOI:10.1017/s1474748023000312

Jonas Stelzig, Scott O. Wilson

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引用次数: 0

Abstract

This paper introduces a generalization of the

$dd^c$

-condition for complex manifolds. Like the

$dd^c$

-condition, it admits a diverse collection of characterizations, and is hereditary under various geometric constructions. Most notably, it is an open property with respect to small deformations. The condition is satisfied by a wide range of complex manifolds, including all compact complex surfaces, and all compact Vaisman manifolds. We show there are computable invariants of a real homotopy type which in many cases prohibit it from containing any complex manifold satisfying such

$dd^c$

-type conditions in low degrees. This gives rise to numerous examples of almost complex manifolds which cannot be homotopy equivalent to any of these complex manifolds.

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超出kÄhler领域的类型条件

本文对复流形的dd^c -条件进行了推广。和dd^c$ -条件一样，它也有各种各样的特征集合，并且在各种几何结构下是遗传的。最值得注意的是，对于小的变形，它是一个开放的性质。满足这一条件的是各种复杂流形，包括所有紧致复杂曲面和所有紧致维斯曼流形。我们证明了实同伦型存在可计算不变量，在许多情况下，这些不变量禁止它在低阶上包含任何满足dd^c$型条件的复流形。这就产生了许多几乎复流形的例子，它们不能同伦等价于这些复流形中的任何一个。

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

Journal of the Institute of Mathematics of Jussieu 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.