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SUMMARY:Julie Desjardins (University of Toronto)
DTSTART:20221117T210000Z
DTEND:20221117T220000Z
DTSTAMP:20260404T132232Z
UID:NTC/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/NTC/3
 /">Torsion points and concurrent lines on Del Pezzo surfaces of degree one
 </a>\nby Julie Desjardins (University of Toronto) as part of Lethbridge nu
 mber theory and combinatorics seminar\n\n\nAbstract\nThe blow up of the an
 ticanonical base point on X\, a del Pezzo surface of degree 1\, gives rise
  to a rational elliptic surface E with only irreducible fibers. The sectio
 ns of minimal height of E are in correspondence with the 240 exceptional c
 urves on X. A natural question arises when studying the configuration of t
 hose curves : \n\nIf a point of X is contained in "many" exceptional curve
 s\, is it torsion on its fiber on E?\n\nIn 2005\, Kuwata proved for del Pe
 zzo surfaces of degree 2 (where there is 56 exceptional curves) that if "m
 any" equals 4 or more\, then yes. In a joint paper with Rosa Winter\, we p
 rove 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.\n
LOCATION:https://stable.researchseminars.org/talk/NTC/3/
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