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Deformations of pairs $ (X,L)$ when $ X$ is singular


Author: Jie Wang
Journal: Proc. Amer. Math. Soc. 140 (2012), 2953-2966
MSC (2010): Primary 14B10, 14B12
DOI: https://doi.org/10.1090/S0002-9939-2011-11230-9
Published electronically: December 29, 2011
MathSciNet review: 2917069
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Abstract: We give an elementary construction of the tangent obstruction theory of the deformations of the pair $ (X,L)$ with $ X$ a reduced local complete intersection scheme and $ L$ a line bundle on $ X$. This generalizes the classical deformation theory of pairs in the case when $ X$ is smooth. A criteria for sections of $ L$ to extend is also given.


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Jie Wang
Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210
Email: jwang@math.ohio-state.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-11230-9
Keywords: Deformations of the pair, tangent obstruction theory, local complete intersection
Received by editor(s): March 18, 2011
Published electronically: December 29, 2011
Communicated by: Lev Borisov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.