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

TL;DR

This paper introduces a new method for constructing mirror pairs of Calabi-Yau threefolds using smoothing of normal crossing varieties composed of quasi-Fano manifolds, supported by conjectures on Landau-Ginzburg models.

Contribution

It presents a novel construction of mirror pairs via smoothing techniques and introduces a new notion of mirror pairs of quasi-Fano manifolds with Calabi-Yau fibrations.

Findings

Constructed 6518 mirror pairs of Calabi-Yau threefolds.

Included 79 self-mirror Calabi-Yau threefolds.

Confirmed Hodge number relations consistent with mirror symmetry.

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.