Néron-Severi groups of product abelian surfaces

Abstract

We give a natural parameterization of the Néron-Severi group of a product $A=E\times E^{\prime }$ 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.

28 pages; revised introduction and added Section 5

Cited by in corpus (1)

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