Abelian Varieties into 2g+1-dim.Linear Systems

Abstract

We show that polarisations of type (1,...,1,2g+2) on g-dimensional abelian varieties are $never$ very ample, if $g\ge 3$. This disproves a conjecture of Debarre, Hulek and Spandaw. We also give a criterion for non-embeddings of abelian varieties into 2g+1-dimensional linear systems.

6 Pages