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SUMMARY:Rosa Winter (MPI MiS)
DTSTART:20201029T163000Z
DTEND:20201029T173000Z
DTSTAMP:20260422T054411Z
UID:SFUQNTAG/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/12/
 ">Density of rational points on a family of del Pezzo surfaces of degree $
 1$</a>\nby Rosa Winter (MPI MiS) as part of SFU NT-AG seminar\n\n\nAbstrac
 t\nDel Pezzo surfaces are classified by their degree d\, which is an integ
 er between $1$ and $9$ (for $d ≥ 3$\, these are the smooth surfaces of d
 egree $d$ 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 Zaris
 ki dense provided that the surface has one $k$-rational point to start wit
 h (that lies outside a specific subset of the surface for degree $2$). How
 ever\, for del Pezzo surfaces of degree $1$ over a field k\, even though w
 e know that they always contain at least one $k$-rational point\, we do no
 t know if the set of $k$-rational points is Zariski dense in general. I wi
 ll talk about a result that is joint work with Julie Desjardins\, in which
  we give necessary and sufficient conditions for the set of $k$-rational p
 oints on a specific family of del Pezzo surfaces of degree $1$ to be Zaris
 ki dense\, where k is a number field. I will compare this to previous resu
 lts.\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/12/
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