Full paper in PDF:
$% A. Arsie, Very ampleness of multiples of principal polarization on degenerate Abelian surfaces, Rev. Mat. Complut. 18 (2005), no. 1, 119–141.%$

Very Ampleness of Multiples of Principal Polarization on Degenerate Abelian Surfaces

Alessandro ARSIE
Dipartimento di Matematica
Università di Bologna
40126 Bologna — Italy
arsie@dm.unibo.it

Received: September 1, 2003
Accepted: June 25, 2004
ABSTRACT

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 .

Key words: very ampleness, degenerate Abelian surface, principal polarization, special projective embeddings.
2000 Mathematics Subject Classification: 14K10; 14J25, 14N05.