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On rationality of the intersection points of a line with a plane quartic | | Roger Oyono
; Christophe Ritzenthaler
; | | Date: |
4 Jun 2010 | | 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. | | Source: | arXiv, 1006.0873 | | Services: | Forum | Review | PDF | Favorites | |
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