Given a two‐generated group of prime‐power order, we investigate the singularities of origamis whose deck group acts transitively and is isomorphic to the given group. Geometric and group‐theoretic ideas are used to classify the possible strata, depending on the prime‐power order. We then show that for many interesting known families of two‐generated groups of prime‐power order, including all regular, or powerful ones, or those of maximal class, each group admits only one possible stratum. However, we also construct examples of two‐generated groups of prime‐power order, which do not determine a unique stratum.
Abelian Covers of ℙ1 of p -Ordinary Ekedahl–Oort Type
Given a family of abelian covers of ${\mathbb{P}}^{1}$ and a prime $p$ of good reduction, by considering the associated Deligne–Mostow Shimura variety, we obtain non-trivial bounds for the Ekedahl–Oort types, and the Newton polygons, at prime $p$ for the curves in the family. In this paper, we investigate whether such bounds are sharp. In particular, we prove sharpness when the number of branching points is at most five and $p$ sufficiently large. Our result is a generalization under stricter assumptions of [ 2, Theorem 6.1] by Bouw, which proves the analogous statement for the $p$-rank, and it relies on the notion of Hasse–Witt triple introduced by Moonen in [ 12].
more » « less- PAR ID:
- 10552974
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- International Mathematics Research Notices
- Volume:
- 2024
- Issue:
- 23
- ISSN:
- 1073-7928
- Format(s):
- Medium: X Size: p. 14369-14392
- Size(s):
- p. 14369-14392
- Sponsoring Org:
- National Science Foundation
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