Let $\mathcal{F}$ be a coherent sheaf over a compact reduced complex space $X$, $L(\mathcal{F})$ the linear fiber space associated with $\mathcal{F}$, $S^{k}(\mathcal{F})$ the k-th symmetric power of $\mathcal{F}$. We show that if the zero-section of $L(\mathcal{F})$ is exceptional, then $H^{r}(X,\mathcal{E} \otimes_{\mathcal{O}_{X}} S^{k}(\mathcal{F})) = 0$ for every coherent sheaf $\mathcal{E}$ on $X$ and for $r \ge 1$ and sufficiently large k. Using this result, we deduce that, if moreover $\operatorname{Supp} \mathcal{F} = X$, then $X$ is a Moišezon space.