Jacobians among abelian threefolds: a geometric approach

Arnaud Beauville (1) , Christophe Ritzenthaler (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 IML - Institut de mathématiques de Luminy

Let A be a principally polarized abelian threefold over a perfect field k, not isomorphic to a product over the algebraic closure of k. There exists a canonical extension k' of k, of degree 1 or 2, such that A becomes isomorphic to a Jacobian over k'. The aim of this note is to give a geometric construction of this extension.

Domaines: Géométrie algébrique [math.AG]

Arnaud Beauville, Christophe Ritzenthaler. Jacobians among abelian threefolds: a geometric approach. Mathematische Annalen, 2011, 350 (4), pp.793-799. ⟨10.1007/s00208-010-0583-6⟩. ⟨hal-00756790⟩