On the Stack of 0-Dimensional Coherent Sheaves: Structural Aspects

doi:10.1017/9781009497206.002

1 - On the Stack of 0-Dimensional Coherent Sheaves: Structural Aspects

Published online by Cambridge University Press: 31 October 2025

Barbara Fantechi and

Andrea T. Ricolfi

Edited by

Pedro L. del Ángel R. ,

Frank Neumann and

Alexander H. W. Schmitt

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Pedro L. del Ángel R.: Affiliation:
Centro de Investigación en Matemáticas
Frank Neumann: Affiliation:
Università di Pavia
Alexander H. W. Schmitt: Affiliation:
Freie Universität Berlin

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Summary

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

Keywords

moduli of coherent sheaves algebraic stacks quot schemes

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Type: Chapter
Information: Moduli, Motives and Bundles
New Trends in Algebraic Geometry
, pp. 1 - 32

DOI: https://doi.org/10.1017/9781009497206.002 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2025

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