Complex algebraic stacks and morphisms of intersection complexes

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Bibliographic Details
Main Author:	Huynh, Matthew
Format:	Preprint
Published:	2024
Subjects:	Algebraic Geometry
Online Access:	Acceder al recurso
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author	Huynh, Matthew
author_facet	Huynh, Matthew
contents	We generalize a construction of Barthel-Brasselet-Fieseler-Gabber-Kaup in the setting of complex varieties to the setting of finite type, complex algebraic stacks. Given two such stacks $\mathcal{X},\mathcal{Y}$ with affine stabilizers, and a morphism between them, we construct a morphism from the pullback of the intersection complex of $\mathcal{Y}$ to the intersection complex of $\mathcal{X}$. As an application, we show that the Borel-Moore fundamental class of a closed substack $\mathcal{Z}$ in a Deligne-Mumford stack $\mathcal{X}$ lifts to a class in the intersection cohomology of $\mathcal{X}$.
format	Preprint
id	arxiv_https___arxiv_org_abs_2403_15890
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Complex algebraic stacks and morphisms of intersection complexes Huynh, Matthew Algebraic Geometry We generalize a construction of Barthel-Brasselet-Fieseler-Gabber-Kaup in the setting of complex varieties to the setting of finite type, complex algebraic stacks. Given two such stacks $\mathcal{X},\mathcal{Y}$ with affine stabilizers, and a morphism between them, we construct a morphism from the pullback of the intersection complex of $\mathcal{Y}$ to the intersection complex of $\mathcal{X}$. As an application, we show that the Borel-Moore fundamental class of a closed substack $\mathcal{Z}$ in a Deligne-Mumford stack $\mathcal{X}$ lifts to a class in the intersection cohomology of $\mathcal{X}$.
title	Complex algebraic stacks and morphisms of intersection complexes
topic	Algebraic Geometry
url	https://arxiv.org/abs/2403.15890

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