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arXiv · 1708.02489

Mirror pairs of Calabi-Yau threefolds from mirror pairs of quasi-Fano threefolds

Nam-Hoon Lee
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Abstract

We present a new construction of mirror pairs of Calabi-Yau manifolds by smoothing normal crossing varieties, consisting of two quasi-Fano manifolds. We introduce a notion of mirror pairs of quasi-Fano manifolds with anticanonical Calabi-Yau fibrations using recent conjectures about Landau-Ginzburg models. Utilizing this notion, we give pairs of normal crossing varieties and show that the pairs of smoothed Calabi-Yau manifolds satisfy the Hodge number relations of mirror symmetry. We consider quasi-Fano threefolds that are some blow-ups of Gorenstein toric Fano threefolds and build 6518 mirror pairs of Calabi-Yau threefolds, including 79 self-mirrors.

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Nam-Hoon Lee. 2017-08-07. Mirror pairs of Calabi-Yau threefolds from mirror pairs of quasi-Fano threefolds. https://doi.org/10.1016/j.matpur.2019.12.007

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