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For any odd integer $d$, we give a presentation for the integral Chow ring of the stack $\mathcal {M}_{0}(\mathbb {P}^r, d)$, as a quotient of the polynomial ring $\mathbb {Z}[c_1,c_2]$. We describe an efficient set of generators for the ideal of relations, and compute them in generating series form. The paper concludes with explicit computations of some examples for low values of $d$ and $r$, and a conjecture for a minimal set of generators.

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.

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The integral Chow ring of $\mathcal {M}_{0}(\mathbb {P}^r, d)$, for $d$ odd

Stacks of cyclic covers of projective spaces

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The integral Chow ring of $\mathcal {M}_{0}(\mathbb {P}^r, d)$, for $d$ odd

Stacks of cyclic covers of projective spaces