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arXiv · 2403.03878

On the stack of 0-dimensional coherent sheaves: structural aspects

Barbara Fantechi·Andrea T. Ricolfi
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Abstract

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 \'etale 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 $\mathcal E\in \mathrm{Coh}(X)$.

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Barbara Fantechi, Andrea T. Ricolfi. 2024-03-06. On the stack of 0-dimensional coherent sheaves: structural aspects. https://arxiv.org/abs/2403.03878

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