[SNU Number Theory Seminar 2022-12-02] Torsion points and concurrent exceptional curves on del Pezzo surfaces of degree one

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일정시작	2022-12-02
배경색상	#FF5733

일정시작

2022-12-02

배경색상

#FF5733

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.

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