Elliptic Fibrations and Involutions on K3 Surfaces

We survey our contributions on the classification of elliptic fibrations on K3 surfaces with a non-symplectic involution. We place them in the more general framework of K3 surfaces with an involution without any hypothesis on its fixed locus or on the action on the symplectic 2-form. We revisit the complete classification of elliptic fibrations on K3 surfaces with a 2-elementary Néron–Severi lattice and give a complete classification of extremal elliptic fibrations on K3 surfaces that are quadratic covers of rational elliptic surfaces.