The Clifford index of line bundles on a 2-elementary K3 surface given by a double cover of a Del Pezzo surface

摘要

We call a K3 surface a 2-elementary K3 surface if the N,ron-Severi lattice satisfies the condition that is a 2-elementary group, where . In this paper, in the case where is a 2-elementary K3 surface given by a double cover of a smooth Del Pezzo surface of degree and is a base point free and big line bundle on , for any smooth curve in the linear system , we investigate line bundles on which compute the Clifford index of C.