K3 SURFACES WITH Z(2)(2) SYMPLECTIC ACTION

摘要

Let G be a finite abelian group which acts symplectically on a K3 surface. The Neron-Severi lattice of the projective K3 surfaces admitting G symplectic action and with minimal Picard number was computed by Garbagnati and Sarti [8]. We consider a four-dimensional family of projective K3 surfaces with Z(2)(2) symplectic action which do not fall into the above cases. If X is one of these K3 surfaces, then it arises as the minimal resolution of a specific Z(2)(3)-cover of P-2 branched along six general lines. We show that the Neron-Severi lattice of X with minimal Picard number is generated by 24 smooth rational curves and that X specializes to the Kummer surface Km(E-i x E-i). We relate X to the K3 surfaces given by the minimal resolution of the Z(2)-cover of P-2, branched along six general lines, and the corresponding Hirzebruch-Kummer covering of exponent 2 of P-2.