论文标题
在变形的胸骨洁面的同时学上
On the deformed Bott-Chern cohomology
论文作者
论文摘要
给定一个紧凑的复杂歧管$ x $和A^{0,1}（x，x，t_ {x}^{1,0}）$中的可集成的beltrami差异$ ϕ \，我们在$ a^{\ a^{\ bulter，\ bulter，\ bulter}（x）$上自然确定$ $ ϕ $并研究其bott-chern cohom omology in $ a^{\ bulter，\ bulter}（x）$上引入了双重复杂结构。特别是，我们建立了针对Bott-Chern共同体的变形理论，并使用它来计算Iwasawa歧管和可行的可行的Nakamura歧管的变形的Bott-Chern共同体。研究了$ \ partial \ bar {\ partial} _ ϕ $ - lemma，我们显示出满足$ \ partial \ bar {\ partial} _ϕ $ - lemmma的紧凑复合歧管。
Given a compact complex manifold $X$ and a integrable Beltrami differential $ϕ\in A^{0,1}(X, T_{X}^{1,0})$, we introduce a double complex structure on $A^{\bullet,\bullet}(X)$ naturally determined by $ϕ$ and study its Bott-Chern cohomology. In particular, we establish a deformation theory for Bott-Chern cohomology and use it to compute the deformed Bott-Chern cohomology for the Iwasawa manifold and the holomorphically parallelizable Nakamura manifold. The $\partial\bar{\partial}_ϕ$-lemma is studied and we show a compact complex manifold satisfying $\partial\bar{\partial}_ϕ$-lemma is formal.
