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arXiv · 1211.4215

Rational points on cubic hypersurfaces that split off two forms

Boqing Xue·Haobo Dai
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Abstract

We show that if $X\subseteq \mathbb{P}^{n-1}$, defined over $\mathbb{Q}$ by a cubic form that splits off two forms, with $n\geq 11$, then $X(\mathbb{Q})$ is non-empty. The same holds for an $(m_1,m_2)$-form with $m_1\geq 4$ and $m_2\geq 5$.

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Boqing Xue, Haobo Dai. 2013-01-09. Rational points on cubic hypersurfaces that split off two forms. https://arxiv.org/abs/1211.4215

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