Rational points on cubic hypersurfaces that split off two forms

Boqing Xue, Haobo Dai

We show that if $X\subseteq {\mathbb{P}}^{n-1}$, defined over $\mathbb{Q}$ by a cubic form that splits off two forms, with $n\ge 11$, then $X(\mathbb{Q})$ is non-empty. The same hol…