  The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians,
among indecomposable principally polarized abelian varieties of dimension g, by
the existence of g+2 points in general position with respect to the principal
polarization, but special with respect to twice the polarization, and
furthermore states that such collections of points must be contained in an
Abel-Jacobi curve. Building on the ideas in the original paper, we give here a
self contained, scheme theoretic proof of the theorem, extending it to finite,
possibly nonreduced subschemes.
