Jacobian elliptic fibrations on K3s with a non‐symplectic automorphism of order 3

Abstract Let be a K3 surface admitting a non‐symplectic automorphism of order 3. Building on work by Garbagnati and Salgado, we classify the Jacobian elliptic fibrations on with respect to the action of on their fibers. If the fiber class of a Jacobian elliptic fibration on is fixed by , we determine the possible configurations of its singular fibers and present the equation for its generic fiber. When the Picard number of is at least 12 and acts trivially on , we apply the Kneser–Nishiyama method to find its Jacobian elliptic fibrations up to ‐equivalence. We use our method to classify them with respect to any non‐symplectic automorphism of order 3 in .