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

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• 作者：Jö ; rg Jahnel^a ; ^{jahnel@mathematik.uni-siegen.de" class="auth_mail" title="E-mail the corresponding author} ; ; Damaris Schindler^b ; ^c ; ^{damaris.schindler@hausdorff-center.uni-bonn.de" class="auth_mail" title="E-mail the corresponding author} ; ^{dschindler@ias.edu" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：primary ; 11G35 ; secondary ; 14G25 ; 14G05 ; 14J26 ; 14J10
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：162
• 期：Complete
• 页码：224-254
• 全文大小：547 K

文摘

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.