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We prove that both classical Chevalley-Warning-Ax and Tsen theorems hold forthe blowing up of a quintic 3-fold along a line of multiplicity 3. Both proofs,which are of the same spirit than the original ones, involve the description ofthis blowing-up as a subvariety of a toric variety.

Arithmetic of rationaly connected quintic 3-folds over finite and function fields