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SUMMARY:Density of rational points on Del Pezzo surfaces of degree one
DTSTART:20121018T111500
DTEND:20121018T123000
DTSTAMP:20260921T115830Z
UID:a33106d3f29cd551c562588e67e85bfcfebac8e8420c966e467c01da
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ronald van Luijk (Leiden University)\nWe state conditions unde
 r which the set of rational points on a Del Pezzo surface of degree one o
 ver a global field is Zariski dense. For example\, it suffices to require
  that the elliptic fibration induced by the anticanonical map has a noda
 l fiber over a rational point of the projective line. It also suffices to
  require the existence of a rational point that does not lie on six exce
 ptional curves of the surface and that has order three on its fiber of the
  elliptic fibration.  This allows us to show that within a parameter sp
 ace for Del Pezzo surfaces of degree one over the real numbers\, the set 
 of those surfaces defined over the rational numbers for which\nthe set of 
 rational points is Zariski dense\, is dense with respect to the real anal
 ytic topology.
LOCATION:AAC006
STATUS:CONFIRMED
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