On the proportion of transverse-free plane curves
نویسندگان
چکیده
We study the asymptotic proportion of smooth plane curves over a finite field Fq which are tangent to every line defined Fq. This partially answers question raised by Charles Favre. Our techniques include applications Poonen's Bertini theorem and Schrijver's on perfect matchings in regular bipartite graphs. main implies that random curve admits transverse Fq-line with very high probability.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2021
ISSN: ['1090-2465', '1071-5797']
DOI: https://doi.org/10.1016/j.ffa.2021.101833