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SUMMARY:Rosa Winter (King's College London)
DTSTART:20211111T130000Z
DTEND:20211111T140000Z
DTSTAMP:20260423T021345Z
UID:ZAG/163
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/163/">Co
 ncurrent exceptional curves on del Pezzo surfaces of degree one and torsio
 n points on elliptic fibrations</a>\nby Rosa Winter (King's College London
 ) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nLet S be
  a del Pezzo surface of degree one. Then S contains 240 exceptional curves
  over an algebraically closed field. After blowing up a specific point one
  obtains an elliptic surface E\, where the exceptional curves correspond t
 o 240 sections. At most 16 exceptional curves gan go through the same poin
 t on S\, and when this happens\, the corresponding point on E is torsion o
 n its fiber. In this talk I will consider the question how many exceptiona
 l curves can go through a point on S for which the corresponding point on 
 E is non-torsion on its fiber. First of all I will explain how this questi
 on came up when studying the density of the set of rational points on del 
 Pezzo surfaces of degree one. I will then show that if at least 9 exceptio
 nal curves intersect in a point on~S\, the corresponding point on E is tor
 sion on its fiber. This is less trivial than one might think by looking at
  the Mordell--Weil rank of E. Finally\, in joint work with Julie Desjardin
 s we show that 7 exceptional curves can go through a non-torsion point\, a
 nd the question if 8 exceptional curves can go through a non-torsion point
  is still work in progress. I will show how one might try to tackle this.\
 n
LOCATION:https://researchseminars.org/talk/ZAG/163/
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