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- W2950077324 abstract "We study the rationality of the intersection points of certain lines and smooth plane quartics C defined over F_q. For q geq 127, we prove the existence of a line such that the intersection points with C are all rational. Using another approach, we further prove the existence of a tangent line with the same property as soon as the characteristic of F_q is different from 2 and q geq 66^2+1. Finally, we study the probability of the existence of a rational flex on C and exhibit a curious behavior when the characteristic of F_q is equal to 3." @default.
- W2950077324 created "2019-06-27" @default.
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- W2950077324 date "2010-06-04" @default.
- W2950077324 modified "2023-09-24" @default.
- W2950077324 title "On rationality of the intersection points of a line with a plane quartic" @default.
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