We construct del Pezzo surfaces of degree violating the Hasse principle explained by the Brauer-Manin obstruction. Using these del Pezzo surfaces, we show that there are algebraic families of surfaces violating the Hasse principle explained by the Brauer-Manin obstruction. Various examples are given.
Nous construisons des surfaces de del Pezzo de degré violant le principe de Hasse expliqué par l’obstruction de Brauer-Manin. En utilisant ces surfaces de del Pezzo de degré , nous montrons qu’il y a des familles algébriques de surfaces violant le principe de Hasse expliqué par l’obstruction de Brauer-Manin. Divers exemples sont donnés.
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DOI: 10.5802/jtnb.805
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@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/} }
TY - JOUR TI - The arithmetic of certain del Pezzo surfaces and K3 surfaces JO - Journal de Théorie des Nombres de Bordeaux PY - 2012 DA - 2012/// SP - 447 EP - 460 VL - 24 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.805/ UR - https://zbmath.org/?q=an%3A1268.14020 UR - https://www.ams.org/mathscinet-getitem?mr=2950701 UR - https://doi.org/10.5802/jtnb.805 DO - 10.5802/jtnb.805 LA - en ID - JTNB_2012__24_2_447_0 ER -
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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