We extend the construction of the normal cone of a closed embedding of schemes to any locally off finite type morphism of higher Artin stacks and show that in the Deligne-Mumford case our construction recovers the relative intrinsic normal cone of Behrend and Fantechi. We characterize our extension as the unique one satisfying a short list of axioms,and use it to construct the deformation to the normal cone. As an application of our methods, we associate to any morphism of Artin stacks equipped with a choice of a global perfect obstruction theory a relative virtual fundamental class in the Chow group of Kresch.

The Intrinsic Normal Cone For Artin Stacks / Aranha, Dhyan. - (2019 Dec 16).

The Intrinsic Normal Cone For Artin Stacks

Aranha, Dhyan
2019-12-16

Abstract

We extend the construction of the normal cone of a closed embedding of schemes to any locally off finite type morphism of higher Artin stacks and show that in the Deligne-Mumford case our construction recovers the relative intrinsic normal cone of Behrend and Fantechi. We characterize our extension as the unique one satisfying a short list of axioms,and use it to construct the deformation to the normal cone. As an application of our methods, we associate to any morphism of Artin stacks equipped with a choice of a global perfect obstruction theory a relative virtual fundamental class in the Chow group of Kresch.
Fantechi, Barbara
Aranha, Dhyan
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Descrizione: PhD Thesis
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/105336
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