On the Arithmetic of Del Pezzo Surfaces of Degree
نویسندگان
چکیده
— We study the arithmetic of certain Del Pezzo surfaces of degree 2. We produce examples of Brauer-Manin obstruction to the Hasse principle, coming from 2and 4-torsion elements in the Brauer group.
منابع مشابه
On the Arithmetic of Del Pezzo Surfaces of Degree 2
Del Pezzo surfaces are smooth projective surfaces, isomorphic over the algebraic closure of the base ,eld to P P or the blow-up of P in up to eight points in general position. In the latter case the del Pezzo surface has degree equal to 9 minus the number of points in the blow-up. The arithmetic of del Pezzo surfaces over number ,elds is an active area of investigation. It is known that the Has...
متن کاملRecent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces
— We survey the state of affairs for the distribution of Q-rational points on non-singular del Pezzo surfaces of low degree, highlighting the recent resolution of Manin’s conjecture for a non-singular del Pezzo surface of degree 4 by la Bretèche and Browning [3].
متن کاملResent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces
We survey the state of affairs for the distribution of Q-rational points on non-singular del Pezzo surfaces of low degree, highlighting the recent resolution of Manin's conjecture for a non-singular del Pezzo surface of degree 4 by la Bretèche and Browning [3].
متن کاملThe arithmetic of certain del Pezzo surfaces and K3 surfaces
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.
متن کامل