Over an algebraically closed field of characteristic 0, the automorphism group of a curve with simple Jacobian must be cyclic of prime-power or two-prime order, a generalized quaternion group, or trivial, and every such group occurs.
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Automorphism groups of curves with simple Jacobians
Over an algebraically closed field of characteristic 0, the automorphism group of a curve with simple Jacobian must be cyclic of prime-power or two-prime order, a generalized quaternion group, or trivial, and every such group occurs.