Jacobians among Abelian threefolds: a formula of Klein and a question of Serre

Gilles Lachaud, Christophe Ritzenthaler, Alexey Zykin

Let k be a field and f be a Siegel modular form of weight h \geq 0 and genus g>1 over k. Using f, we define an invariant of the k-isomorphism class of a principally polarized abeli…