2012/06/22 by Shilin Yu, Yu, Shilin
Mathematics · #14B20 #18D20 (Primary) #18E30 #58A20 (Secondary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.DG #msc:14B20 #msc:18D20 #msc:18E30 #msc:58A20
paper · pdf · doi:10.48550/arxiv.1206.5155
47 pages. Introduction and abstract rewritten. MSC and keywords added
openalex publication_date 2012/06/22 · arxiv created 2013/03/03 · arxiv updated 2013/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by a work of Kapranov, 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 complex 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. 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.