Deformation theory from the point of view of fibered categories
Deformation theory from the point of view of fibered categories
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从纤维范畴的角度看变形理论
DOI：
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发表时间：
2010
期刊：
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通讯作者：
Angelo Vistoli
中科院分区：
文献类型：
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作者：
Mattia Talpo;Angelo Vistoli
我们用纤维范畴的语言而不是更传统的函子语言来阐述形变理论的形式方面。主要概念有形变问题的切线空间、障碍理论、逆形变和泛形式形变。我们给出了两个关键结果的证明：本文中的施莱辛格定理的一个版本，以及关于障碍的Ran-Kawamata消失定理。同时，我们对三种重要的情形进行了详细的分析：光滑变元、局部完全交子格式和相干层。
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.