  In this paper we prove the $\Gamma_{00}$ conjecture of van Geemen and van der
Geer, under the additional assumption that the matrix of coefficients of the
tangent has rank at most 2. This assumption is satisfied by Jacobians, and thus
our result gives a characterization of the locus of Jacobians among all
principally polarized abelian varieties.
  The proof is by reduction to the (stronger version of the) characterization
of Jacobians by semidegenerate trisecants, i.e. by the existence of lines
tangent to the Kummer variety at one point and intersecting it in another,
proven by Krichever in the course of his proof of the Welters' trisecant
conjecture.
