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Stacks of cyclic covers of projective spaces

Published online by Cambridge University Press:  04 December 2007

Alessandro Arsie  and
Angelo Vistoli
Alessandro Arsie
Affiliation:
Dipartimento di Matematica, Università di Bologna, 40126 Bologna, [email protected], [email protected]
Angelo Vistoli
Affiliation:
Dipartimento di Matematica, Università di Bologna, 40126 Bologna, [email protected], [email protected]
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Abstract

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We define stacks of uniform cyclic covers of Brauer–Severi schemes, proving that they can be realized as quotient stacks of open subsets of representations, and compute the Picard group for the open substacks parametrizing smooth uniform cyclic covers. Moreover, we give an analogous description for stacks parametrizing triple cyclic covers of Brauer–Severi schemes of rank 1 that are not necessarily uniform, and give a presentation of the Picard group of the substacks corresponding to smooth triple cyclic covers.

Keywords

algebraic stacksBrauer–Severi schemesequivariant Chow ringsPicard groupsquotient stacksuniform cyclic covers14A2014C2214D20
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 3 , May 2004 , pp. 647 - 666
Copyright
Foundation Compositio Mathematica 2004