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

Abstract

Let $X$ be a compact complex manifold, and let $\pi: \mathcal{X} \rightarrow B$ 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.