Algebra & Number Theory
- Algebra Number Theory
- Volume 13, Number 1 (2019), 1-18.
Ordinary algebraic curves with many automorphisms in positive characteristic
Let be an ordinary (projective, geometrically irreducible, nonsingular) algebraic curve of genus defined over an algebraically closed field of odd characteristic . Let be the group of all automorphisms of which fix elementwise. For any solvable subgroup of we prove that . There are known curves attaining this bound up to the constant . For odd, our result improves the classical Nakajima bound and, for solvable groups , the Gunby–Smith–Yuan bound where for some positive constant .
Algebra Number Theory, Volume 13, Number 1 (2019), 1-18.
Received: 25 October 2016
Revised: 18 October 2018
Accepted: 20 November 2018
First available in Project Euclid: 27 March 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14H37: Automorphisms
Secondary: 14H05: Algebraic functions; function fields [See also 11R58]
Korchmáros, Gábor; Montanucci, Maria. Ordinary algebraic curves with many automorphisms in positive characteristic. Algebra Number Theory 13 (2019), no. 1, 1--18. doi:10.2140/ant.2019.13.1. https://projecteuclid.org/euclid.ant/1553652019