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On the number of certain del Pezzo surfaces of degree four violating the Hasse principle

Author:
Jahnel, J?rg   Schindler, Damaris  


Journal:
Journal of Number Theory


Issue Date:
2016


Abstract(summary):

Abstract

We give an asymptotic expansion for the density of del Pezzo surfaces of degree four in a certain Birch Swinnerton-Dyer family violating the Hasse principle due to a Brauer–Manin obstruction. Under the assumption of Schinzel's hypothesis and the finiteness of Tate–Shafarevich groups for elliptic curves, we obtain an asymptotic formula for the number of all del Pezzo surfaces in the family, which violate the Hasse principle.



Page:
224-254


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