Deformation theory from the point of view of fibered categories
File(s)
Accepted version
Author(s)
Talpo, Mattia
Vistoli, Angelo
Type
Working Paper
Abstract
We give an exposition of the formal aspects of deformation theory in the
language of fibered categories, instead of the more traditional one of
functors. The main concepts are that of tangent space to a deformation problem,
obstruction theory, versal and universal formal deformations. We include proofs
of two key results: a versione of Schlessinger's Theorem in this context, and
the Ran--Kawamata vanishing theorem for obstructions. We accompany this with a
detailed analysis of three important cases: smooth varieties, local complete
intersection subschemes and coherent sheaves.
language of fibered categories, instead of the more traditional one of
functors. The main concepts are that of tangent space to a deformation problem,
obstruction theory, versal and universal formal deformations. We include proofs
of two key results: a versione of Schlessinger's Theorem in this context, and
the Ran--Kawamata vanishing theorem for obstructions. We accompany this with a
detailed analysis of three important cases: smooth varieties, local complete
intersection subschemes and coherent sheaves.
Date Issued
2011-01-31
Citation
2011
Publisher
arXiv
Copyright Statement
©2011The Author(s).
Identifier
http://arxiv.org/abs/1006.0497v2
Subjects
math.AG
math.AG
14D15 (Primary) 14B10 (Secondary)
Notes
corrected several typos and made some minor improvements to the exposition
Publication Status
Published