Abelian surfaces with a (1,2) polarization and full level-2 structure

Abstract: Abstract: The moduli threefold of principally polarized abelian surfaces with full level-2 structure is well understood thanks to its close connection with the moduli space $M_{0,6}$ of six points on ${\bf P}^1$. The moduli threefolds of (1,d)-polarized surfaces with d>1 are more elusive. We report on our recent work on the d=2 case with full level-2 structure. Here the moduli threefold is still rational, and comes with an action of a group G isomorphic with ${\rm Aut}(S_4^2)$ instead of $S_6$. We use elliptic fibrations of the Kummer surface to give several models of this moduli threefold together with the G-action.

algebraic geometrynumber theory

Audience: researchers in the discipline

MIT number theory seminar

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