Algebraic Geometry Working Seminar

Monday, August 9, 2021 11:00 am - 11:00 am EDT

Nicholas Banks, Department of Pure Mathematics, University of Waterloo

"Galois Actions on Surfaces of Small Picard Rank"

In this talk, we compute actions of the absolute Galois group of the rational numbers on the Picard groups of smooth rational projective surfaces up to Picard rank four. We accomplish this by computing the effective and nef cones of said surfaces; this determines the possible Galois actions, since the minimal generators of these cones are permuted by said action. This is motivated by David McKinnon's 2007 conjecture concerning rational approximations to rational points on varieties. Specifically, this conjecture states that if a rational point on a variety lies on a rational curve, then the best approximations to that point also lie on a rational curve. Since Galois-invariant curves are defined over the rationals, computing these actions will provide information about the rational curves in question.

Zoom meeting:

  • Meeting ID: 811 2094 8164
  • Passcode: 033003