Espaces fibrés linéaires faiblement négatifs sur un espace complexe

Abstract:

Let F be a coherent sheaf over a compact reduced complex space $X,L(\text {F})$ the linear fibre space associated with F, ${S^k}(\text {F})$ the kth symmetric power of F. We show that if the zero-section of $L(\text {F})$ is exceptional, then ${H^r}(X,\text {E}{ \otimes _{{O_X}}}{S^k}(\text {F})) = 0$ 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.