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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Density of rational points on Del Pezzo surfaces o
f degree one - Ronald van Luijk (Leiden)
DTSTART;TZID=Europe/London:20130213T141500
DTEND;TZID=Europe/London:20130213T151500
UID:TALK42154AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/42154
DESCRIPTION:We state conditions under which the set of rationa
l points\non a Del Pezzo surface of degree one ove
r an infinite field is\nZariski dense. For example
\, it suffices to require that the elliptic\nfibra
tion induced by the anticanonical map has\na nodal
fiber over a rational point of the projective lin
e. It also suffices to\nrequire the existence of a
rational point that does not lie on six\nexceptio
nal curves of the surface and that has order three
on its fiber of the\nelliptic fibration. This al
lows us to show that within a parameter\nspace for
Del Pezzo surfaces of degree one over the real nu
mbers\,\nthe set of those surfaces defined over th
e rational numbers for which\nthe set of rational
points is Zariski dense\, is dense with respect to
the real\nanalytic topology. We also state condit
ions that may be satisfied for every\ndel Pezzo su
rface and that can be verified with a finite compu
tation\nfor any del Pezzo surface that does satisf
y them. This is joint work\nwith Cecilia Salgado.\
n
LOCATION:MR 13\, CMS
CONTACT:Caucher Birkar
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