The arithmetic of certain del Pezzo surfaces and K3 surfaces
Dong Quan Ngoc Nguyen1
1 Department of Mathematics The University of Arizona, 617 N. Santa Rita Ave, Tucson, Arizona 85721, USA
Journal de Théorie des Nombres de Bordeaux, Volume 24 (2012) no. 2, pp. 447-460.

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.

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.

Received:
Published online:
DOI: 10.5802/jtnb.805
Dong Quan Ngoc Nguyen 1

1 Department of Mathematics The University of Arizona, 617 N. Santa Rita Ave, Tucson, Arizona 85721, USA 
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Dong Quan Ngoc Nguyen. The arithmetic of certain del Pezzo surfaces and K3 surfaces. Journal de Théorie des Nombres de Bordeaux, Volume 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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