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 $\pi :\mathcal{X}\to B$ be a small deformation of $X$, the dimensions of the Bott-Chern cohomology groups $H_{\mathrm{BC}}^{p,q}(X(t))$ and Aeppli cohomology groups $H_{\mathrm{A}}^{p,q}(X(t))$ 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.

arXiv admin note: text overlap with arXiv:0704.1977

References in corpus (1)

• Autour de la cohomologie de Bott-Chern