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Abstract: We give an exposition of the formal aspects of deformation theory in thelanguage of fibered categories, instead of the more traditional one offunctors. The main concepts are that of tangent space to a deformation problem,obstruction theory, versal and universal formal deformations. We include proofsof two key results: a versione of Schlessinger-s Theorem in this context, andthe Ran-Kawamata vanishing theorem for obstructions. We accompany this with adetailed analysis of three important cases: smooth varieties, local completeintersection subschemes and coherent sheaves.



Author: Mattia Talpo, Angelo Vistoli

Source: https://arxiv.org/



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