Sharp Bertini Theorem for Plane Curves over Finite Fields
2019 ◽
Vol 62
(02)
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pp. 223-230
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Keyword(s):
AbstractWe 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 $q=p^{r}$ .
2010 ◽
Vol 130
(11)
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pp. 2528-2541
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2013 ◽
Vol 12
(3)
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pp. 651-676
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2001 ◽
Vol 27
(4)
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pp. 197-200
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1990 ◽
Vol 33
(3)
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pp. 282-285
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2018 ◽
Vol 49
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pp. 80-93
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1999 ◽
Vol 2
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pp. 118-138
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