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

by qsms posted Nov 28, 2022
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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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