Abstract
Inspired by a work of Kapranov (Kap99), we define the notion of Dolbeault complex of the formal neighborhood of a closed embedding of complex manifolds. This construction allows us to study coherent sheaves over the formal neighborhood via com- plex analytic approach, as in the case of usual complex manifolds and their Dolbeault complexes. Moreover, our the Dolbeault complex as a differential graded algebra can be associated with a dg-category according to Block (Blo10). We show this dg-category is a dg-enhancement of the bounded derived category over the formal neighborhood under the assumption that the submanifold is compact. This generalizes a similar result of Block in the case of usual complex manifolds. CONTENTS
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