六维近凯勒流形的Kodaira维数  

Kodaira Dimension of Nearly Kähler 6-manifolds

作　　者：陈豪杰 王冠明 Hao Jie CHEN;Guan Ming WANG(Department of Mathematics,Zhejiang Normal University,Jirihua 321004,P.R.China)

机构地区：[1]浙江师范大学数学系,金华321004

出　　处：《数学学报（中文版）》2021年第1期87-98,共12页Acta Mathematica Sinica：Chinese Series

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)。

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.We investigate the canonical bundle and Kodaira dimension of nearly Kähler 6-manifolds.We prove that the canonical bundle of a strictly nearly K?hler 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 CP^3 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 h^1,0,h^2,0,h^2,3,h^1,3 of the homogeneous strictly nearly Kähler F^3 and CP^3 are all zeros.

关 键 词：近凯勒流形 典范丛 Kodaira维数 近复流形 

分 类 号：O186.1[理学—基础数学]