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

Espaces fibrés linéaires faiblement négatifs sur un espace complexe