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

1998/10/19 by Klaus Hulek, Kristian Ranestad, Hulek, Klaus +1
Mathematics · #14K10 (Primary) 14J32 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J32 #msc:14K10

paper · pdf · doi:10.48550/arxiv.math/9810120

41 pages

arxiv created 1998/10/19 · arxiv updated 2009/11/30

Abstract

(1,d)-polarized abelian surfaces in P^(d-1) with two plane cubic curve fibrations lie in two elliptic P²-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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