六维近凯勒流形的Kodaira维数

陈豪杰, 王冠明

数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 87-98.

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数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 87-98. DOI: 10.12386/A2021sxxb0007
论文

六维近凯勒流形的Kodaira维数

    陈豪杰, 王冠明
作者信息 +

Kodaira Dimension of Nearly Kähler 6-manifolds

    Hao Jie CHEN, Guan Ming WANG
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文章历史 +

摘要

本文主要研究了六维近凯勒流形的典范丛和Kodaira维数.证明了六维严格近凯勒流形的典范丛是拟全纯平凡的，从而其Kodaira维数为0.特别地，证明了三维复射影空间CP3具有Kodaira维数不为-∞的近复结构.对于齐性的六维严格近凯勒流形，具体构造了它们典范丛的整体生成元.证明了齐性近凯勒流形F3和CP3的Hodge数h1，0，h2，0，h2，3，h1，3均为零.

Abstract

We investigate the canonical bundle and Kodaira dimension of nearly Kähler 6-manifolds. We prove that the canonical bundle of a strictly nearly Kähler 6-manifold is pseudoholomorphically trivial. Therefore, the Kodaira dimension is zero. As a corollary, we show the existence of non-integrable almost complex structure on CP3 whose Kodaira dimension is not -∞. We also construct explicit generating sections of the canonical bundle of homogeneous strictly nearly Kähler 6-manifolds and prove that the Hodge numbers h1,0, h2,0, h2,3, h1,3 of the homogeneous strictly nearly Kähler F3 and CP3 are all zeros.

关键词

近凯勒流形 / 典范丛 / Kodaira维数 / 近复流形

Key words

Nearly Kähler manifolds / canonical bundle / Kodaira dimension / almost complex manifolds

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陈豪杰, 王冠明. 六维近凯勒流形的Kodaira维数. 数学学报, 2021, 64(1): 87-98 https://doi.org/10.12386/A2021sxxb0007
Hao Jie CHEN, Guan Ming WANG. Kodaira Dimension of Nearly Kähler 6-manifolds. Acta Mathematica Sinica, Chinese Series, 2021, 64(1): 87-98 https://doi.org/10.12386/A2021sxxb0007

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基金

国家自然科学基金资助项目（11901530）；浙江省自然科学基金资助项目（LY19A010017）
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