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Monodromy of hyperplane sections of curves and decomposition statistics over finite fields
Alexei Entin, Monodromy of Hyperplane Sections of Curves and Decomposition Statistics over Finite Fields, arXiv:1805.05454v3, 31 March 2019. The paper first appeared on arXiv in May 2018 and was published in International Mathematics Research Notices 2021 (14), 10409–10441. The edition read here is arXiv v3; no comparison with the journal edition has been made.
Theorem 1 counts the Frobenius conjugacy classes of hyperplane sections of a quasireflexive curve whose components over the finite field are absolutely irreducible. The section domain requires exactly as many distinct geometric intersection points as the curve's degree. It is not a condition merely on the rational points of the intersection. The main term is the conjugacy-class proportion in the product of the component symmetric groups; the relative error is of order , uniformly at fixed ambient dimension and total degree.
Section 2 defines quasireflexivity using a simple tangent on each component of the whole curve. Proposition 2.1 identifies it with reflexivity in characteristic different from two. Its proof invokes the generic order of contact theorem and the Segre–Wallace criterion.
Read status: claims checked; proofs read for structure only. Theorem 1 with its definitions, and Section 2 through Proposition 2.1 and its short proof, were read in the v3 TeX. The main counting and monodromy proofs, the cited contact and separability proofs, and the later applications remain unread. This reading supplies no independent proof certification.
Bears on. The plane-curve specialization underlies the Frobenius count used for blocking sets, and therefore the conditional curve approximation route to Problem 1159. It does not provide the required approximation of arbitrary minimal blocking sets.
The arXiv record, read on 2026-10-17, gives the non-exclusive distribution license. No file of this source is held because no license on record permits redistribution.