Vol. 13, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Ordinary algebraic curves with many automorphisms in positive characteristic

Gábor Korchmáros and Maria Montanucci

Vol. 13 (2019), No. 1, 1–18

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.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

algebraic curves, algebraic function fields, positive characteristic, automorphism groups
Mathematical Subject Classification 2010
Primary: 14H37
Secondary: 14H05
Received: 25 October 2016
Revised: 18 October 2018
Accepted: 20 November 2018
Published: 13 February 2019
Gábor Korchmáros
Dipartimento di Matematica, Informatica ed Economia
Università degli Studi della Basilicata
Maria Montanucci
Dipartimento di Tecnica e Gestione dei Sistemi Industriali
Università degli Studi di Padova