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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Espaces fibrés linéaires faiblement négatifs sur un espace complexe


Author: Vincenzo Ancona
Journal: Trans. Amer. Math. Soc. 215 (1976), 45-61
MSC: Primary 32L10
DOI: https://doi.org/10.1090/S0002-9947-1976-0430332-3
MathSciNet review: 0430332
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Abstract: 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.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0430332-3
Keywords: Puissance symétrique, espace fibré linéaire faiblement négatif, faisceau faiblement positif, espace de Moišezon
Article copyright: © Copyright 1976 American Mathematical Society

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