On the stack of 0-dimensional coherent sheaves: structural aspects
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929331312263168 |
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| author | Fantechi, Barbara Ricolfi, Andrea T. |
| author_facet | Fantechi, Barbara Ricolfi, Andrea T. |
| contents | Let $X$ be a quasiprojective scheme. In this expository note we collect a series of useful structural results on the stack $\mathscr{C}oh^n(X)$ parametrising $0$-dimensional coherent sheaves of length $n$ over $X$. For instance, we discuss its functoriality (in particular its behaviour along étale maps), the support morphism to $\mathrm{Sym}^n(X)$, and its relationship with the Quot scheme of points $\mathrm{Quot}_X(\mathcal E,n)$ for fixed $\mathcal E\in \mathrm{Coh}(X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the stack of 0-dimensional coherent sheaves: structural aspects Fantechi, Barbara Ricolfi, Andrea T. Algebraic Geometry Let $X$ be a quasiprojective scheme. In this expository note we collect a series of useful structural results on the stack $\mathscr{C}oh^n(X)$ parametrising $0$-dimensional coherent sheaves of length $n$ over $X$. For instance, we discuss its functoriality (in particular its behaviour along étale maps), the support morphism to $\mathrm{Sym}^n(X)$, and its relationship with the Quot scheme of points $\mathrm{Quot}_X(\mathcal E,n)$ for fixed $\mathcal E\in \mathrm{Coh}(X)$. |
| title | On the stack of 0-dimensional coherent sheaves: structural aspects |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.03878 |