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arXiv · 1510.04733

Random hypersurfaces and embedding curves in surfaces over finite fields

Joseph Gunther
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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.

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Joseph Gunther. 2015-10-15. Random hypersurfaces and embedding curves in surfaces over finite fields. https://arxiv.org/abs/1510.04733

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