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arXiv · 1809.04930

An application of Bertini Theorem

Mehdi Makhul·Josef Schicho
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Abstract

Given an irreducible variety $X$ over a finite field, the density of hypersurfaces of varying degree $d$ intersecting $X$ in an irreducible subvariety is $1$, by a result of Charles and Poonen. In this note, we analyse the situation fixing $d=1$ and extend the base field instead of the degree $d$. We compute the probability that a random linear subspace of the right dimension intersects $X$ in a given number of points.

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Mehdi Makhul, Josef Schicho. 2018-09-13. An application of Bertini Theorem. https://arxiv.org/abs/1809.04930

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