Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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On the geometry of the projection of torsion points of an elliptic curve into projective line

Fedor Bogomolov

created by risa on 28 Mar 2017

7 apr 2017 -- 15:30

Aula Dal Passo, Dip.Matematica, Università "Tor Vergata", Roma

Abstract.

In this lecture I introduce and discuss geometry of subsets of points in $P^1$ obtained as projections of torsion point of elliptic curves. We consider standard degree two projections $\pi$ on $P^1$. If two elliptic curves $E_1,E_2$ have different ramification sets in $P^1$ then the intersections of the images of torsion points is finite number. In fact for many pairs of elliptic curves such intersection is trivial or consists of just one point. We conjecture that there is universal constant bounding such intersections independently of the curves involved (universal boundedness). However it is possible to get rather big intersection. The maximal intersection obtained so far is $22$. I explain in my lecture both the main tools to construct examples of pairs of elliptic curves where the intersection is big and the reasons for existing of a realistic universal bound for such an intersection.

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