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SUMMARY:Density of rational points on Del Pezzo surfaces of degree one - R
 onald van Luijk (Leiden)
DTSTART:20130213T141500Z
DTEND:20130213T151500Z
UID:TALK42154@talks.cam.ac.uk
CONTACT:Caucher Birkar
DESCRIPTION:We state conditions under which the set of rational points\non
  a Del Pezzo surface of degree one over an infinite field is\nZariski dens
 e. For example\, it suffices to require that the elliptic\nfibration induc
 ed by the anticanonical map has\na nodal fiber over a rational point of th
 e projective line. It also suffices to\nrequire the existence of a rationa
 l point that does not lie on six\nexceptional curves of the surface and th
 at has order three on its fiber of the\nelliptic fibration.  This allows u
 s to show that within a parameter\nspace for Del Pezzo surfaces of degree 
 one over the real numbers\,\nthe set of those surfaces defined over the ra
 tional numbers for which\nthe set of rational points is Zariski dense\, is
  dense with respect to the real\nanalytic topology. We also state conditio
 ns that may be satisfied for every\ndel Pezzo surface and that can be veri
 fied with a finite computation\nfor any del Pezzo surface that does satisf
 y them. This is joint work\nwith Cecilia Salgado.\n
LOCATION:MR 13\, CMS
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