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On the deformed Bott-Chern cohomology
Journal of Geometry and Physics ( IF 1.6 ) Pub Date : 2021-04-15 , DOI: 10.1016/j.geomphys.2021.104250
Wei Xia

Given a compact complex manifold X and a integrable Beltrami differential ϕA0,1(X,TX1,0), we introduce a double complex structure on A,(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 ¯ϕ-lemma is studied and we show a compact complex manifold satisfying ¯ϕ-lemma is formal.



中文翻译:

关于变形的Bott-Chern同调

给定一个紧凑的复流形X和一个可积的Beltrami微分ϕ一种01个XŤX1个0,我们在上引入了双重复杂结构 一种X自然地确定φ,并研究其博特-陈省身上同调。特别地,我们建立了Bott-Chern同调的变形理论,并用它来计算Iwasawa流形和全纯可并行化Nakamura流形的Bott-Chern形变。这¯ϕ研究了-引理,并证明了满足 ¯ϕ-引理是正式的。

更新日期:2021-04-20
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