Rational points on some Fano cubic bundles

Victor V. Batyrev, Yuri Tschinkel

We consider some families of smooth Fano hypersurfaces $X_{n+2}$ in ${\mathbf{P}}^{n+2}\times {\mathbf{P}}^3$ given by a homogeneous polynomial of bidegree $(1,3)$. For these varieties we o…