ULethbridge Number Theory and Combinatorics Seminar: Julie Desjardins
Event Recap
This event took place via zoom. A recording is available on mathtube.org. For more information, contact Félix Baril Boudreau or Bobby Miraftab.
Topic
Torsion points and concurrent lines on Del Pezzo surfaces of degree one
Details
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, is it 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. In a joint paper with Rosa Winter, we prove that for del Pezzo surfaces of degree 1, if “many” equals 9 or more, then yes. Moreover, we find counterexamples where a torsion point lies at the intersection of 7 exceptional curves.