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arXiv · 1804.01569

Sharp Bertini theorem for plane curves over finite fields

Shamil Asgarli
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Abstract

We prove that if $C$ is a reflexive smooth plane curve of degree $d$ defined over a finite field $\mathbb{F}_q$ with $d\leq q+1$, 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 $2p+1$ where $q=p^{r}$.

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Shamil Asgarli. 2018-04-04. Sharp Bertini theorem for plane curves over finite fields. https://doi.org/10.4153/cmb-2018-018-0

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