Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Kazemifard, Ahmad, Tafazolian, Saeed
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220653018