Abelian surfaces in toric 4-folds

Abstract

We investigate the possibility of embedding minimal abelian surfaces in smooth toric 4-folds with Picard number 2. The existence of such an embedding imposes conditions on the 4-fold, which we partly describe. On the other hand, we exhibit such embeddings in a special case, using a simple description of morphisms into smooth toric varieties.

19 pages, 1 figures, plain TeX with epsf. Typos corrected and referenced updated