Abelian surfaces with two plane cubic curve fibrations and Calabi-Yau threefolds

Details Abelian surfaces with two plane cubic curve fibrations and Calabi-Yau threefolds Abelian surfaces with two plane cubic curve fibrations and Calabi-Yau threefolds

1998-10-19

arxiv.org/abs/math/9810120v1

Mathematics

Algebraic Geometry

41 pages

Scientific paper

(1,d)-polarized abelian surfaces in P^(d-1) with two plane cubic curve fibrations lie in two elliptic P^2-scrolls. The union of these scrolls form a reducible Calabi-Yau 3-fold. In this paper we show that this occurs when d<10 and analyse the family of such surfaces and 3-folds in detail when d=6. In particular, the reducible Calabi-Yau 3-folds deform in that case to irreducible ones with non-normal singularities.

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