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arXiv · alg-geom/9602013

Rational points on some Fano cubic bundles

Victor V. Batyrev·Yuri Tschinkel
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Abstract

We consider some families of smooth Fano hypersurfaces $X_{n+2}$ in ${\bf P}^{n+2} \times {\bf P}^3$ given by a homogeneous polynomial of bidegree $(1,3)$. For these varieties we obtain lower bounds for the number of $F$-rational points of bounded anticanonical height in arbitrary nonempty Zariski open subset $U \subset X_{n+2}$. These bounds contradict previous expectations about the distribution of $F$-rational points of bounded height on Fano varieties.

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BibTeXRIS

Victor V. Batyrev, Yuri Tschinkel. 1996-02-17. Rational points on some Fano cubic bundles. https://arxiv.org/abs/alg-geom/9602013

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