Abelian surfaces with two plane cubic curve fibrations and Calabi-Yau threefolds
Algebraic Geometry
2007-05-23 v1
Abstract
(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.
Keywords
Cite
@article{arxiv.math/9810120,
title = {Abelian surfaces with two plane cubic curve fibrations and Calabi-Yau threefolds},
author = {Klaus Hulek and Kristian Ranestad},
journal= {arXiv preprint arXiv:math/9810120},
year = {2007}
}
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41 pages