2 research outputs found
The geometry of flex tangents to a cubic curve and its parameterizations
International audienceWe show how the study of the geometry of the nine flex tangents to a cubic produces many pseudo-parameterizations, including the ones given by Icart, Kammerer, Lercier, Renault and Farashahi
The geometry of some parameterizations and encodings
We explore parameterizations by radicals of low genera algebraic curves. We
prove that for a prime power that is large enough and prime to , a fixed
positive proportion of all genus 2 curves over the field with elements can
be parameterized by -radicals. This results in the existence of a
deterministic encoding into these curves when is congruent to modulo
. We extend this construction to parameterizations by -radicals for
small odd integers , and make it explicit for