Transverse Kahler structures on central foliations of complex manifolds
Transverse Kahler structures on central foliations of complex manifolds
复制标题
复杂流形中心叶状结构上的横向卡勒结构
DOI：
10.1007/s10231-018-0762-8
复制
发表时间：
2019
影响因子：
1
通讯作者：
Hiroaki Ishida Hisashi Kasuya
中科院分区：
文献类型：
--
作者：
菊田 伸;Shin Kikuta;菊田伸;菊田伸;菊田伸;Shin Kikuta;Shin Kikuta;Shin Kikuta;Shi Kikuta;菊田 伸;菊田 伸;菊田 伸;Hiroaki Ishida Hisashi Kasuya
对于紧致复流形，我们引入了与自同构群的某些交换子群相关联的全纯叶理。如果在这样的叶理上存在横Kähler结构，那么我们得到一个与de Rham复形拟同构的微分分次代数和一个与Dolbeault复形拟同构的微分双分次代数，就像紧致Kähler流形的形式一样.此外，在一定的附加条件下，我们可以将Morgan的混合Hodge结构理论发展为类似于光滑代数簇的研究。
For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. If there exists a transverse Kähler structure on such a foliation, then we obtain a nice differential graded algebra which is quasi-isomorphic to the de Rham complex and a nice differential bi-graded algebra which is quasi-isomorphic to the Dolbeault complex like the formality of compact Kähler manifolds. Moreover, under certain additional condition, we can develop Morgan’s theory of mixed Hodge structures as similar to the study on smooth algebraic varieties.