On the jumping phenomenon of ${\dim }_{\mathbb{C}}{H}^q({\mathcal{X}}_t,{\mathcal{E}}_t)$

Kwokwai Chan, Yat-Hin Suen

Let $X$ be a compact complex manifold and $E$ be a holomorphic vector bundle on $X$. Given a deformation $(\mathcal{X},\mathcal{E})$ of the pair $(X,E)$ over a small polydisk $B$ c…