THE BOUNDARY OF THE p-RANK $0$ 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 $\ell =3$ an...

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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 Cambridge, UK Cambridge University Press 01.12.2022
Subjects
Codes
14H37
14D20
14H30
14H40
11G20
14K10
14H10
11G10
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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