Espaces fibrés linéaires faiblement négatifs sur un espace complexe

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