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arXiv · 1507.03869

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

Jörg Jahnel·Damaris Schindler
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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.

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Jörg Jahnel, Damaris Schindler. 2015-07-14. On the number of certain Del Pezzo surfaces of degree four violating the Hasse principle. https://arxiv.org/abs/1507.03869

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