Very ampleness of multiples of principal polarization on degenerate Abelian surfaces.
Quite recently, Alexeev and Nakamura proved that if Y is a stable semi-Abelic variety (SSAV) of dimension g equipped with the ample line bundle O(1), which deforms to a principally polarized Abelian variety, then O(n) is very ample as soon as n ≥ 2g + 1, that is n ≥ 5 in the case of surfaces. Here it is proved, via elementary methods of projective geometry, that in the case of surfaces this bound can be improved to n ≥ 3.