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

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 MSC: 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. (C) 2019 Elsevier Masson SAS. All rights reserved.