THE BOUNDARY OF THE p -RANK STRATUM OF THE MODULI SPACE OF CYCLIC COVERS OF THE PROJECTIVE LINE

We study the p -rank stratification of the moduli space of cyclic degree $\ell $ covers of the projective line in characteristic p for distinct primes p and $\ell $ . The main result is about the intersection of the p -rank $0$ stratum with the boundary of the moduli space of curves. When $\ell =3$...

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Bibliographic Details
Published inNagoya mathematical journal Vol. 248; pp. 865 - 887
Main Authors OZMAN, EKIN, PRIES, RACHEL, WEIR, COLIN
Format Journal Article
LanguageEnglish
Published 01.12.2022
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Summary:We study the p -rank stratification of the moduli space of cyclic degree $\ell $ covers of the projective line in characteristic p for distinct primes p and $\ell $ . The main result is about the intersection of the p -rank $0$ stratum with the boundary of the moduli space of curves. When $\ell =3$ and $p \equiv 2 \bmod 3$ is an odd prime, we prove that there exists a smooth trielliptic curve in characteristic p , for every genus g , signature type $(r,s)$ , and p -rank f satisfying the clear necessary conditions.
ISSN:0027-7630
2152-6842
DOI:10.1017/nmj.2022.12