Geodesic
Sharp Bertini Theorem for Plane Curves over Finite Fields
Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 223-230

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DOI

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 $q=p^{r}$.
DOI : 10.4153/CMB-2018-018-0
Mots-clés : Bertini theorem, transversality, finite field 
Asgarli, Shamil. Sharp Bertini Theorem for Plane Curves over Finite Fields. Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 223-230. doi: 10.4153/CMB-2018-018-0
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     author = {Asgarli, Shamil},
     title = {Sharp {Bertini} {Theorem} for {Plane} {Curves} over {Finite} {Fields}},
     journal = {Canadian mathematical bulletin},
     pages = {223--230},
     year = {2019},
     volume = {62},
     number = {2},
     doi = {10.4153/CMB-2018-018-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-018-0/}
}
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