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SUMMARY:Xinyu Fang (Harvard University)
DTSTART:20261116T210000Z
DTEND:20261116T220000Z
DTSTAMP:20261115T003416Z
UID:NTBU/60
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTBU/60/">Ga
 lois group of exceptional curves on the generic del Pezzo surface</a>\nby 
 Xinyu Fang (Harvard University) as part of Boston University Number Theory
  Seminar\n\nLecture held in CDS Room 365 in Boston University.\n\nAbstract
 \nWe give a new proof that the Galois action on the $27$ lines on the gene
 ric cubic surface is maximal\, i.e.\, given by the Weyl group $W(E_6)$. Ou
 r proof is uniform for all base fields $k$\; in particular\, the result is
  new when $k$ has characteristic $2$ or $3$. We show an analogous result f
 or the generic del Pezzo surfaces of all degrees.\n\nAs a consequence\, we
  deduce that over any number field or $\\F_q(t)$\, $100\\%$ of cubic surfa
 ces have no Brauer-Manin obstruction. Combined with the recent result that
  the Brauer-Manin obstruction is the only one for cubic surfaces over glob
 al fields of characteristic $p>0$ not equal to $3$\, this implies that $10
 0\\%$ of cubic surfaces over $\\F_q(t)$ with $3\\nmid q$ satisfy the Hasse
  principle.\n
LOCATION:https://researchseminars.org/talk/NTBU/60/
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