BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Rosa Winter (Max Planck Institute for Mathematics in the Sciences 
 (Leipzig))
DTSTART:20210219T150000Z
DTEND:20210219T160000Z
DTSTAMP:20260423T023047Z
UID:zorp_1729/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/zorp_1729/6/
 ">Density of rational points on a family of del Pezzo surfaces of  degree 
 1</a>\nby Rosa Winter (Max Planck Institute for Mathematics in the Science
 s (Leipzig)) as part of ZORP (zoom on rational points)\n\n\nAbstract\nDel 
 Pezzo surfaces are surfaces classified by their degree $d$\, which is an i
 nteger between 1 \nand 9 (for $d\\geq 3$\, these are the smooth surfaces o
 f degree $d$ in $\\mathbb{P}^d$). For del Pezzo surfaces of degree at leas
 t $2$ over a field $k$\, we know that the set of $k$-rational points is Za
 riski 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 thoug
 h we know that they always contain at least one $k$-rational point\, we do
  not know if the set of $k$-rational points is Zariski dense in general. I
  will talk about a result that is joint work with Julie Desjardins\, in wh
 ich we give sufficient conditions for the set of $k$-rational points on a 
 specific family of del Pezzo surfaces of degree 1 to be Zariski dense\, wh
 ere $k$ is any infinite field of characteristic 0. These conditions are ne
 cessary if $k$ is finitely generated over $\\mathbb{Q}$. I will compare th
 is to previous results.\n
LOCATION:https://researchseminars.org/talk/zorp_1729/6/
END:VEVENT
END:VCALENDAR