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

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

2011-04-27

arxiv.org/abs/1104.5159v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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