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.

Schaffler, L. (2018). K3 SURFACES WITH $\mathbb{Z}_2^2$ SYMPLECTIC ACTION. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 48(7), 2347-2383 [10.1216/RMJ-2018-48-7-2347].

K3 SURFACES WITH $\mathbb{Z}_2^2$ SYMPLECTIC ACTION

Schaffler, L
2018-01-01

Abstract

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.
Schaffler, L. (2018). K3 SURFACES WITH $\mathbb{Z}_2^2$ SYMPLECTIC ACTION. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 48(7), 2347-2383 [10.1216/RMJ-2018-48-7-2347].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/423928
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