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On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures
International Journal of Mathematics ( IF 0.6 ) Pub Date : 2021-07-24 , DOI: 10.1142/s0129167x21500750
Andrea Cattaneo 1 , Antonella Nannicini 2 , Adriano Tomassini 3
Affiliation  

The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact 4-dimensional solvmanifolds without any integrable almost complex structure. According to the classification theory we consider: 𝔯𝔯3,1, 𝔫𝔦𝔩4 and 𝔯4,λ,(1+λ) with 1 < λ < 1 2. For the first solvmanifold we introduce special families of almost complex structures, compute the corresponding Kodaira dimension and show that it is no longer a deformation invariant. Moreover, we prove Ricci flatness of the canonical connection for the almost Kähler structure. Regarding the other two manifolds we compute the Kodaira dimension for certain almost complex structures. Finally, we construct a natural hypercomplex structure providing a twistorial description.

中文翻译:

关于几乎没有复杂结构的复杂 4 维解流形的 Kodaira 维数

本文的目的是继续研究几乎复杂流形的 Kodaira 维数,重点是紧致的情况4维解流形,没有任何可积的几乎复结构。根据分类理论,我们认为:𝔯𝔯3,-1,𝔫𝔦𝔩4𝔯4,λ,-(1+λ) - 1 < λ < -1 2. 对于第一个求解流形,我们引入了几乎复杂结构的特殊族,计算相应的 Kodaira 维数并证明它不再是变形不变量。此外,我们证明了几乎 Kähler 结构的规范连接的 Ricci 平坦度。关于其他两个流形,我们计算某些几乎复杂结构的 Kodaira 维数。最后,我们构建了一个提供扭曲描述的自然超复杂结构。
更新日期:2021-07-24
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