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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2403.15890 |
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| _version_ | 1866913778971443200 |
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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 |