Rational points on some Fano cubic bundles

Details Rational points on some Fano cubic bundles Rational points on some Fano cubic bundles

1996-02-17

arxiv.org/abs/alg-geom/9602013v1

Mathematics

Algebraic Geometry

8 pages., LaTeX

Scientific paper

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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