Zariski-van Kampen method and transcendental lattices of certain singular K3 surfaces

Mathematics – Algebraic Geometry

Scientific paper

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24 pages, typos are corrected, references are updated, a new figure is added

Scientific paper

We present a method of Zariski-van Kampen type for the calculation of the transcendental lattice of a complex projective surface. As an application, we calculate the transcendental lattices of complex singular K3 surfaces associated with an arithmetic Zariski pair of maximizing sextics of type $A_{10}+A_{9}$ that are defined over a real quadratic field and are conjugate to each other over the field of rational numbers.

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