Abstract
Let K be an algebraically closed field of characteristic p > 0, and let X be a curve over K of genus g ≥ 2. Assume that the automorphism group Aut(X) of X over K fixes no point of X. The following result is proven. If there is a point P on X whose stabilizer in Aut (X) contains a p-subgroup of order greater than gp/(p— 1), then X is birationally equivalent over K to one of the irreducible plane curves (II), (III), (IV), (V) listed in the Introduction.
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