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 OY(1), which deforms to a principally polarized Abelian variety, then OY(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.
@article{urn:eudml:doc:44539,
title = {Very ampleness of multiples of principal polarization on degenerate Abelian surfaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {18},
year = {2005},
pages = {119-141},
zbl = {1076.14055},
mrnumber = {MR2135535},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44539}
}
Arsie, Alessandro. Very ampleness of multiples of principal polarization on degenerate Abelian surfaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 18 (2005) pp. 119-141. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44539/