Algebra & Number Theory

Ordinary algebraic curves with many automorphisms in positive characteristic

Gábor Korchmáros and Maria Montanucci

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Let X be an ordinary (projective, geometrically irreducible, nonsingular) algebraic curve of genus g(X)2 defined over an algebraically closed field K of odd characteristic p. Let Aut(X) be the group of all automorphisms of X which fix K elementwise. For any solvable subgroup G of Aut(X) we prove that |G|34(g(X)+1)32. There are known curves attaining this bound up to the constant 34. For p odd, our result improves the classical Nakajima bound |G|84(g(X)1)g(X) and, for solvable groups G, the Gunby–Smith–Yuan bound |G|6(g(X)2+1221g(X)32) where g(X)>cp2 for some positive constant c.

Article information

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H37: Automorphisms
Secondary: 14H05: Algebraic functions; function fields [See also 11R58]

algebraic curves algebraic function fields positive characteristic automorphism groups


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.

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