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arXiv · 1311.4960

Bertini irreducibility theorems over finite fields

François Charles·Bjorn Poonen
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Abstract

Given a geometrically irreducible subscheme X in P^n over F_q of dimension at least 2, we prove that the fraction of degree d hypersurfaces H such that the intersection of H and X is geometrically irreducible tends to 1 as d tends to infinity. We also prove variants in which X is over an extension of F_q, and in which the immersion of X in P^n is replaced by a more general morphism.

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François Charles, Bjorn Poonen. 2013-11-20. Bertini irreducibility theorems over finite fields. https://doi.org/10.1090/s0894-0347-2014-00820-1

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