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Faisceaux\(\bar{\partial}\)-cohérents sur les variétés complexes

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Dans ce travail nous généralisons au contexte des faisceaux analytiques cohérents un résultat classique de Koszul–Malgrange (Koszul and Malgrange in Arch Math 9 : 102–109, 1958) concernant l’intégrabilité des connexions de type (0,1) sur un fibré vectoriel complexe C au-dessus d’une variété complexe. En introduisant la notion de faisceau \(\bar{\partial}\)-cohérent, qui est une notion qui vit dans le contexte C , nous montrons l’existence d’une équivalence (exacte) entre la catégorie des faisceaux analytiques cohérents et la catégorie des faisceaux \(\bar{\partial}\)-cohérents. Une application de notre caractérisation est une méthode (la \(\bar{\partial}\)-stabilité) qui permet de trouver des structures analytiques par déformation C d’autres structures analytiques.

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Correspondence to Nefton Pali.

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Pali, N. Faisceaux\(\bar{\partial}\)-cohérents sur les variétés complexes. Math. Ann. 336, 571–615 (2006). https://doi.org/10.1007/s00208-006-0010-1

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  • DOI: https://doi.org/10.1007/s00208-006-0010-1

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