2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148386We prove that a 1-dimnl family of abelian varieties with an ample sheaf defining principal polarization can be canonically compactified (after a finite base change) to a projective family with an ample sheaf. We show that the central fiber (P,L), which we call an SQAV, has a canonical Cartier theta divisor. We give a combinatorial definition for SQAVs and describe their geometrical properties, in particular compute cohomologies of L^n, n\ge0.Final version, to appear in Tohoku Math. JAlgebraic Geometry14text