Bertini irreducibility theorems over finite fields
Abstract
Given a geometrically irreducible subscheme X in Pn over Fq 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 Fq, and in which the immersion of X in Pn is replaced by a more general morphism.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.