- Date : 2022-12-02 (Fri) 10:00 AM
Place : Zoom 910 1345 711, Passcode 331303
- Speaker : Julie Desjardins (University of Toronto)
- Title : Torsion points and concurrent exceptional curves on del Pezzo surfaces of degree one
- Abstract :
The blow up of the anticanonical base point on X, a del Pezzo surface of degree 1, gives rise to a rational elliptic surface E with only irreducible fibers. The sections of minimal height of E are in correspondence with the 240 exceptional curves on X. A natural question arises when studying the configuration of those curves :
If a point of X is contained in « many » exceptional curves, it is torsion on its fiber on E?
In 2005, Kuwata proved for del Pezzo surfaces of degree 2 (where there is 56 exceptional curves) that if « many » equals 4 or more, then yes. With Rosa Winter, we prove that for del Pezzo surfaces of degree 1, if « many » equals 9 or more, then yes. Additionnally we find counterexamples where a torsion point lies at the intersection lies at the intersection of 7 exceptional curves.