Plane Curves Admitting a Non-classical Automorphism

An automorphism of a projective curve over an algebraically closed field is said to be non-classical, if the image of any smooth point under the automorphism lies on the tangent line at the point. This paper shows that in characteristic zero, there does not exist a smooth plane curve admitting a non-classical automorphism. This result is a generalization of results according to Levcovitz in 1991. This paper also considers the relation between non-classical automorphisms and Galois points.