Hilbert schemes of points

Fantechi, Barbara; Göttsche, Lothar; Illusie, Luc; Kleiman, Steven L.; Nitsure, Nitin; Vistoli, Angelo

doi:10.1090/surv/123/07

Cited by 5 publications

(1 citation statement)

References 20 publications

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“…The theorem is essentially due to Mori, and largely follows the argument presented in [10, Proposition 2.A.11] and [5,Lemma 6.3.3]. We include the argument here partly for convenience, and partly because the use of successive obstruction spaces make our statement slightly more general, although the adjustment to the argument is straightforward.…”

Section: But This Is Corollary 236 (Vi)mentioning

confidence: 99%

Deformations and automorphisms: a framework for globalizing local tangent and obstruction spaces

Osserman¹

2010

Annali Scuola Normale Superiore - Classe Di Scienze

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Building on Schlessinger's work, we define a framework for studying geometric deformation problems which allows us to systematize the relationship between the local and global tangent and obstruction spaces of a deformation problem. Starting from Schlessinger's functors of Artin rings, we proceed in two steps: we replace functors to sets by categories fibered in groupoids, allowing us to keep track of automorphisms, and we work with deformation problems naturally associated to a scheme X , and which naturally localize on X , so that we can formalize the local behavior. The first step is already carried out by Rim in the context of his homogeneous groupoids, but we develop the theory substantially further. In this setting, many statements known for a range of specific deformation problems can be proved in full generality, under very general stack-like hypotheses.

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Section: But This Is Corollary 236 (Vi)mentioning

confidence: 99%