Automorphisms of the Generalized Fermat curves

Aristides Kontogeorgis, Panagiotis Paramantzoglou

Published 2014-09-10Version 1

The automorphism group of the generalized Fermat $F_{k,n}$ curves is studied. We use tools from the theory of complete projective intersections in order to prove that every automorphism of the curve can be extended to an automorphism of the ambient projective space. In particular if $k-1$ is not a power of the characteristic, then a conjecture of of Y. Fuertes, G. Gonz\'alez-Diez, R. Hidalgo, M. Leyton is proved.