Large p-group actions with a p-elementary abelian derived group

Let k be an algebraically closed field of characteristic p>0 and C a connected nonsingular projective curve over k with genus g⩾2. Let (C,G) be a “big action,” i.e. a pair (C,G) where G is a p-subgroup of the k-automorphism group of C such that . The aim of this paper is to describe the big actions whose derived group G′ is p-elementary abelian. In particular, we obtain a structure theorem for the functions parametrizing the Artin–Schreier cover C→C/G′. Using Artin–Schreier duality, we shift to a group-theoretic point of view to characterize relevant cases. Then, we display universal families and discuss the corresponding deformation space for p=5.