Rational points on some Fano cubic bundles

Abstract

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 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.

8 pages., LaTeX

Cited by in corpus (22)

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