The arithmetic of certain del Pezzo surfaces and K3 surfaces
Dong Quan Ngoc Nguyen
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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DOI : https://doi.org/10.5802/jtnb.805 
@article{JTNB_2012__24_2_447_0,
     author = {Dong Quan Ngoc Nguyen},
     title = {The arithmetic of certain del {Pezzo} surfaces and {K3} surfaces},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {447--460},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {24},
     number = {2},
     year = {2012},
     doi = {10.5802/jtnb.805},
     zbl = {1268.14020},
     mrnumber = {2950701},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.805/}
}
Dong Quan Ngoc Nguyen. The arithmetic of certain del Pezzo surfaces and K3 surfaces. Journal de Théorie des Nombres de Bordeaux, Tome 24 (2012) no. 2, pp. 447-460. doi : 10.5802/jtnb.805. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.805/

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