Smooth hypersurface sections containing a given subscheme over a finite field
Algebraic Geometry
2017-04-03 v1 Number Theory
Abstract
We use the "closed point sieve" to prove a variant of a Bertini theorem over finite fields. Specifically, given a smooth quasi-projective subscheme X of P^n of dimension m over F_q, and a closed subscheme Z in P^n such that Z intersect X is smooth of dimension l, we compute the fraction of homogeneous polynomials vanishing on Z that cut out a smooth subvariety of X. The fraction is positive if m>2l.
Cite
@article{arxiv.1012.0628,
title = {Smooth hypersurface sections containing a given subscheme over a finite field},
author = {Bjorn Poonen},
journal= {arXiv preprint arXiv:1012.0628},
year = {2017}
}
Comments
7 pages. This paper appeared a few years ago. (I'm posting it in response to a request for the TeX file.)