On the Hasse principle for del Pezzo surfaces of degrees 3 and 4

Abstract: 

In this talk, I report about del Pezzo surfaces of degree 4 and cubic surfaces that violate the Hasse principle. The historically first such examples were constructed by Swinnerton-Dyer. Recently, we proved that counterexamples to the Hasse principle are in fact Zariski dense in the respective moduli spaces. This work was joint with Damaris Schindler and Andreas-Stephan Elsenhans.