Dimension jumps in Bott–Chern and Aeppli cohomology groups

Jiezhu Lin and Xuanming Ye

Vol. 273 (2015), No. 2, 461–482

DOI: 10.2140/pjm.2015.273.461

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 $H_{BC}^{p,q}\left(X\left(t\right)\right)$ and Aeppli cohomology groups $H_A^{p,q}\left(X\left(t\right)\right)$ may vary under this deformation. In this paper, we will study the deformation obstructions of a $\left(p,q\right)$ 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.

Keywords

Bott–Chern cohomology, Aeppli cohomology, deformation, obstruction, Kodaira–Spencer classes

Mathematical Subject Classification 2010

Primary: 14B12, 14C30, 14F05, 14F40, 18G40

Milestones

Received: 6 March 2014

Revised: 27 July 2014

Accepted: 15 August 2014

Published: 23 December 2014