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Cyclic automorphisms beyond the canonical bound
Abstract
Let X be a smooth projective curve of genus g >= 2 over an algebraically closed field K, and suppose that Aut(X) contains a cyclic subgroup G of order N > 2g - 2. The cases N >= 2g + 1 are known. We treat the two boundary values N = 2g and N = 2g - 1. In the tame case we obtain an explicit finite list of ramification signatures. In odd characteristic we prove that the Sylow p-subgroup of G has order p and determine all wild boundary cases by a direct ramification analysis; the resulting curves are Artin-Schreier-Kummer fiber products. In characteristic two we prove that the 2-part has order at most four and classify all wild boundary cases, including Artin-Schreier-Witt normal forms for the C4 and C12 cases.
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BibTeX
@misc{kazemifard2026cyclic,
title = {{Cyclic automorphisms beyond the canonical bound}},
author = {Ahmad Kazemifard and Saeed Tafazolian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04702},
eprint = {2610.04702},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04702},
}
RIS
TY - UNPB
TI - Cyclic automorphisms beyond the canonical bound
AU - Ahmad Kazemifard
AU - Saeed Tafazolian
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04702
UR - https://arxiv.org/abs/2610.04702
AB - Let X be a smooth projective curve of genus g >= 2 over an algebraically closed field K, and suppose that Aut(X) contains a cyclic subgroup G of order N > 2g - 2. The cases N >= 2g + 1 are known. We treat the two boundary values N = 2g and N = 2g - 1. In the tame case we obtain an explicit finite list of ramification signatures. In odd characteristic we prove that the Sylow p-subgroup of G has order p and determine all wild boundary cases by a direct ramification analysis; the resulting curves are Artin-Schreier-Kummer fiber products. In characteristic two we prove that the 2-part has order at most four and classify all wild boundary cases, including Artin-Schreier-Witt normal forms for the C4 and C12 cases.
ER -