On a Conjecture of Serre on Abelian Threefolds
نویسنده
چکیده
A conjecture of Serre predicts a precise from of Torelli Theorem for genus 3 curves, namely, an indecomposable principally polarized abelian threefold is a Jacobian if and only if some specific invariant is a square. We study here a three dimensional family of such threefolds, introduced by Howe, Leprevost and Poonen. By a new formulation, we link their results to the conjecture of Serre. Then, we recover a formula of Klein related to the conjecture for complex threefolds. In this case the invariant is a modular form of weight 18, and the conjecture is proved using theta functions identities.
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