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SUMMARY:Nils Bruin (Simon Fraser University)
DTSTART:20220929T223000Z
DTEND:20220929T233000Z
DTSTAMP:20260422T054251Z
UID:SFUQNTAG/70
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/70/
 ">Twists of the Burkhardt quartic threefold</a>\nby Nils Bruin (Simon Fras
 er University) as part of SFU NT-AG seminar\n\n\nAbstract\nA basic example
  of a family of curves with level structure is the Hesse pencil of ellipti
 c curves:\n\\[x^3+y^3+z^3+ \\lambda xyz = 0\,\\]\nwhich gives a family of 
 elliptic curves with labelled 3-torsion points. The parameter $\\lambda$ i
 s a parameter on the corresponding moduli space.\n\nThe analogue for genus
  2 curves is given by the Burkhardt quartic threefold. In this talk\, we w
 ill go over some of its interesting geometric properties. In an arithmetic
  context\, where one considers a non-algebraically closed base field\, it 
 is also important to consider the different possible <em>twists</em> of th
 e space. We will discuss an interesting link with a so-called <em>field of
  definition obstruction</em> that occurs for genus 2 curves\, and see that
  this obstruction has interesting consequences for the existence of ration
 al points on certain twists of the Burkhardt quartic.\n\nThis talk is base
 d on joint works with my students Brett Nasserden and Eugene Filatov.\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/70/
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