Random hypersurface sections over finite fields are shown to avoid positive-dimensional singular loci with probability at least 1 - O((d+1)^r p^{-ceil(d/2)}), proving Poonen's arithmetic Bertini conjecture.
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Frobenius-orbit slicing and uniform elimination of positive-dimensional singular loci
Random hypersurface sections over finite fields are shown to avoid positive-dimensional singular loci with probability at least 1 - O((d+1)^r p^{-ceil(d/2)}), proving Poonen's arithmetic Bertini conjecture.