A family of varieties with exactly one pointless rational fiber

Abstract

We construct a concrete example of a 1-parameter family of smooth projective geometrically integral varieties over an open subscheme of P^1_Q such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.

arXiv comment4 pages. Some stylistic changes, replaced an argument in Lemma 3.1 with a simpler argument as suggested by the referee. To appear in J. Théor. Nombres Bordeaux

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