Random hypersurfaces and embedding curves in surfaces over finite fields
Number Theory
2016-06-09 v2 Algebraic Geometry
Abstract
We use Poonen's closed point sieve to prove two independent results. First, we show that the obvious obstruction to embedding a curve in a smooth surface is the only obstruction over a perfect field, by proving the finite field analogue of a Bertini-type result of Altman and Kleiman. Second, we prove a conjecture of Vakil and Wood on the asymptotic probability of hypersurface sections having a prescribed number of singularities.
Cite
@article{arxiv.1510.04733,
title = {Random hypersurfaces and embedding curves in surfaces over finite fields},
author = {Joseph Gunther},
journal= {arXiv preprint arXiv:1510.04733},
year = {2016}
}
Comments
9 pages; to appear in Journal of Pure and Applied Algebra