| 六维近凯勒流形的Kodaira维数 |
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| 引用本文： | 陈豪杰,王冠明.六维近凯勒流形的Kodaira维数[J].数学学报,2021,64(1):87-98. |
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| 作者姓名： | 陈豪杰 王冠明 |
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| 作者单位： | 浙江师范大学数学系 金华 321004 |
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| 基金项目： | 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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| 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CP^3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F^3和CP^3的Hodge数h^1,0,h^2,0,h^2,3,h^1,3均为零.
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| 关 键 词： | 近凯勒流形 典范丛 Kodaira维数 近复流形 |
Kodaira Dimension of Nearly Kähler 6-manifolds |
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| Hao Jie CHEN,Guan Ming WANG.Kodaira Dimension of Nearly Kähler 6-manifolds[J].Acta Mathematica Sinica,2021,64(1):87-98. |
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| Authors: | Hao Jie CHEN Guan Ming WANG |
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| Institution: | Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China |
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| 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. |
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| Keywords: | Nearly Kähler manifolds canonical bundle Kodaira dimension almost complex manifolds |
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