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Fibrations in non-simply connected Calabi-Yau quotients. (English) Zbl 1396.83041

Summary: In this work we study genus one fibrations in Calabi-Yau three-folds with a non-trivial first fundamental group. The manifolds under consideration are constructed as smooth quotients of complete intersection Calabi-Yau three-folds (CICYs) by a freely acting, discrete automorphism. By probing the compatibility of symmetries with genus one fibrations (that is, discrete group actions which preserve a local decomposition of the manifold into fiber and base) we find fibrations that are inherited from fibrations on the covering spaces. Of the 7,890 CICY three-folds, 195 exhibit known discrete symmetries, leading to a total of 1,695 quotient manifolds. By scanning over 20,700 fiber/symmetry pairs on the covering spaces we find 17,161 fibrations on the quotient Calabi-Yau manifolds. It is found that the vast majority of the non-simply connected manifolds studied exhibit multiple different genus one fibrations – echoing a similar ubiquity of such structures that has been observed in other data sets. The results are available at [M. Gross, Duke Math. J. 74, No. 2, 271–299 (1994; Zbl 0838.14033)]. The possible base manifolds are all singular and are catalogued. These Calabi-Yau fibrations generically exhibit multiple fibers and are of interest in F-theory as backgrounds leading to theories with superconformal loci and discretely charged matter.

MSC:

83E30 String and superstring theories in gravitational theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
53Z05 Applications of differential geometry to physics
81T60 Supersymmetric field theories in quantum mechanics

Citations:

Zbl 0838.14033

Software:

CICY Quotients
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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