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SUMMARY:Rosa Winter
DTSTART:20211117T150000Z
DTEND:20211117T160000Z
DTSTAMP:20260418T063841Z
UID:LNTS/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/55/">De
 nsity of rational points on del Pezzo surfaces of degree 1</a>\nby Rosa Wi
 nter as part of London number theory seminar\n\nLecture held in Huxley 144
 \, Imperial.\n\nAbstract\nDel Pezzo surfaces are surfaces classified by th
 eir degree $d$\, which is an integer between 1 and 9 (for $d\\geq3$\, thes
 e are the smooth surfaces of degree $d$ in $\\mathbb{P}^d$). For del Pezzo
  surfaces of degree at least 2 over a field $k$\, we know that the set of 
 $k$-rational points is Zariski dense provided that the surface has one $k$
 -rational point to start with (that lies outside a specific subset of the 
 surface for degree 2). However\, for del Pezzo surfaces of degree 1 over a
  field $k$\, even though we know that they always contain at least one $k$
 -rational point\, we do not know if the set of $k$-rational points is Zari
 ski dense in general. I will talk about a result that is joint work with J
 ulie Desjardins\, in which we give sufficient conditions for the set of $k
 $-rational points on a specific family of del Pezzo surfaces of degree 1 t
 o be Zariski dense\, where $k$ is any infinite field of characteristic 0. 
 These conditions are necessary if $k$ is finitely generated over $\\mathbb
 {Q}$. I will compare this to previous results.\n
LOCATION:https://researchseminars.org/talk/LNTS/55/
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