Stacks of cyclic covers of projective spaces

Details Stacks of cyclic covers of projective spaces Stacks of cyclic covers of projective spaces

2003-01-02

arxiv.org/abs/math/0301008v2

Mathematics

Algebraic Geometry

23 pages; some minor changes; to appear in Compositio Mathematica

Scientific paper

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, which are not necessarily uniform, and give a presentation of the Picard group for substacks corresponding to smooth triple cyclic covers.

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