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

2024/03/06 by Fantechi, Barbara, Ricolfi, Andrea T. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.03878

Abstract

Let X be a quasiprojective scheme. In this expository note we collect a series of useful structural results on the stack \mathscrCohⁿ(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 Symⁿ(X), and its relationship with the Quot scheme of points Quot_X(\mathcal E,n) for fixed \mathcal E∈ Coh(X).

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