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Transactions of the American Mathematical Society

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The Dolbeault dga of a formal neighborhood


Author: Shilin Yu
Journal: Trans. Amer. Math. Soc. 368 (2016), 7809-7843
MSC (2010): Primary 18D20; Secondary 14B20, 18E30, 58A20
DOI: https://doi.org/10.1090/tran6646
Published electronically: June 10, 2016
MathSciNet review: 3546785
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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.


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Additional Information

Shilin Yu
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Email: shilinyu@math.upenn.edu

DOI: https://doi.org/10.1090/tran6646
Keywords: Formal neighborhoods, derived categories, differential graded algebras, differential graded categories
Received by editor(s): March 3, 2013
Received by editor(s) in revised form: December 8, 2014
Published electronically: June 10, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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