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

2015/07/14 by Jahnel, Jörg, Schindler, Damaris
#14G05 #14J10 #14J26 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary 11G35 #Secondary 14G25

paper · doi:10.48550/arxiv.1507.03869

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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