2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106403In this paper we study the automorphisms group of some $K3$ surfaces which are double covers of the projective plane ramified over a smooth sextic plane curve. More precisely, we study the case of a $K3$ surface of Picard rank two such that there is a rational curve of degree $d$ which is tangent to the sextic in $d$ points.10 pages, LaTex. The e-mail address of the second author has been correctedAlgebraic Geometry14J28text