The arithmetic of certain del Pezzo surfaces and K3 surfaces

Nguyen, Dong Quan Ngoc

Journal de théorie des nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 447-460.

Nous construisons des surfaces de del Pezzo de degré $4$ violant le principe de Hasse expliqué par l’obstruction de Brauer-Manin. En utilisant ces surfaces de del Pezzo de degré $4$, nous montrons qu’il y a des familles algébriques de surfaces $K3$ violant le principe de Hasse expliqué par l’obstruction de Brauer-Manin. Divers exemples sont donnés.

We construct del Pezzo surfaces of degree $4$ violating the Hasse principle explained by the Brauer-Manin obstruction. Using these del Pezzo surfaces, we show that there are algebraic families of $K3$ surfaces violating the Hasse principle explained by the Brauer-Manin obstruction. Various examples are given.

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