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arXiv · 1403.0285

The jumping phenomenon of the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups

Jiezhu Lin·Xuanming Ye
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Abstract

Let $X$ be a compact complex manifold, and let $π: \mathcal{X} \rightarrow B$ be a small deformation of $X$, the dimensions of the Bott-Chern cohomology groups $H_{\rm BC}^{p,q}(X(t))$ and Aeppli cohomology groups $H_{\rm A}^{p,q}(X(t))$ may vary under this deformation. In this paper, we will study the deformation obstructions of a $(p,q)$ class in the central fiber $X$. In particular, we obtain an explicit formula for the obstructions and apply this formula to the study of small deformations of the Iwasawa manifold.

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Jiezhu Lin, Xuanming Ye. 2014-03-06. The jumping phenomenon of the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups. https://arxiv.org/abs/1403.0285

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