%0 Journal Article
%T N¨Śron-Severi groups of product abelian surfaces
%A Julian Rosen
%A Ariel Shnidman
%J Mathematics
%D 2014
%I arXiv
%X We give a natural parameterization of the N\'eron-Severi group of a product $A = E\times E'$ of two elliptic curves in terms of quadratic forms. As an application, we determine (in the non-CM case) whether $A$ contains a smooth curve of any fixed genus. We also determine whether $A$ admits a very ample line bundle of any fixed degree. In particular, we determine which of these abelian surfaces embed in $\mathbb{P}^4$, i.e. which come from the Horrocks-Mumford bundle.
%U http://arxiv.org/abs/1402.2233v2