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Sharp Bertini Theorem for Plane Curves over Finite Fields
Published online by Cambridge University Press: 07 January 2019
Abstract
We prove that if $C$ is a reflexive smooth plane curve of degree
$d$ defined over a finite field
$\mathbb{F}_{q}$ with
$d\leqslant q+1$, then there is an
$\mathbb{F}_{q}$-line
$L$ that intersects
$C$ transversely. We also prove the same result for non-reflexive curves of degree
$p+1$ and
$2p+1$ when
$q=p^{r}$.
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- © Canadian Mathematical Society 2018
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