The Dolbeault dga of a formal neighborhood
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Abstract:
Inspired by a work of Kapranov (1999), we define the notion of a 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 a complex analytic approach, as in the case of usual complex manifolds and their Dolbeault complexes. Moreover, the Dolbeault complex as a differential graded algebra can be associated with a dg-category according to Block (2010). We show that 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.References
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Additional Information
- Shilin Yu
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
- MR Author ID: 1104773
- Email: shilinyu@math.upenn.edu
- Received by editor(s): March 3, 2013
- Received by editor(s) in revised form: December 8, 2014
- Published electronically: June 10, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 7809-7843
- MSC (2010): Primary 18D20; Secondary 14B20, 18E30, 58A20
- DOI: https://doi.org/10.1090/tran6646
- MathSciNet review: 3546785