Large 2-groups of automorphisms of curves with positive 2-rank

2011/04/27 by Giulietti, Massimo, Korchmaros, Gabor
#14H37 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1104.5159

Abstract

Let K be an algebraically closed field of characteristic 2, and let X be a curve over K of genus g>1 and 2-rank r>0. For 2-subgroups S of the K-automorphism group Aut(X) of X, the Nakajima bound is |S| < 4g-3. For every g=2^h+1>8, we construct a curve X attaining the Nakajima bound and determine its relevant properties: X is a bielliptic curve with r=g, and its K-automorphism group has a dihedral K-automorphism group of order 4(g-1) which fixes no point in X. Moreover, we provide a classification of 2-groups S of K-automorphisms not fixing a point of X and such that |S|> 2g-1.

Related

• Large p-groups of automorphisms of algebraic curves in characteristic p
• Large 3-groups of automorphisms of algebraic curves in characteristic 3
• Curves with a large automorphism group admitting a cyclic subgroup of index 2
• Algebraic curves with a large cyclic automorphism group
• Large automorphism groups of ordinary curves in characteristic 2