Transcendental lattices of certain singular K3 surfaces
Abstract
We compute the transcendental lattices of the singular K3 surfaces belonging to three pencils of K3 surfaces, namely the Ap\'ery-Fermi pencil with transcendental lattice U 12 , the Verrill's pencil with transcendental lattice U 6 and another pencil linked to Verrill's pencil with transcendental lattice U 24 . Many corollaries are deduced. For example, some singular K3 surfaces belong to different pencils or are Kummer surfaces of K3 surfaces of another pencil.
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