Zariski-van Kampen method and transcendental lattices of certain singular \(K3\) surfaces (Q841449)

The authors present a Zariski-van Kampen type method to calculate the transcendental lattice of complex projective surfaces. They use this method to calculate the transcendental lattices of a pair of (the minimal resolutions of) double covers of \(\mathbb P^2\) ramified along a sextic with a singularity of type \(A_{10}\) and a singularity of type \(A_9\), defined over \(\mathbb Q(\sqrt{-5})\). Both sextic are conjugated under \(\mathrm{Gal}(\mathbb Q(\sqrt{5})/\mathbb Q)\).