Number Theory Seminar

Speaker: Nils Bruin (Simon Fraser University, Vancouver).

Title: On Abelian surfaces with full 3-level structure.

Abstract: The Burkhardt quartic threefold is known to be birational to the moduli space of abelian surfaces with labeled 3-torsion. It is well-studied over $\mathbb{C}$. We look at various arithmetic subtleties, such as how to descend its birational parametrization to $\mathbb{Q}$. We also investigate how to construct from a (sufficiently general) point on the Burkhardt quartic threefold an explicit genus two curve together with a marking of its three-torsion on its Jacobian. Finally, we investigate how twists of the Burkhardt quartic threefold correspond to twisted 3-level structures and how field-of-definition obstructions interact with these.

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