Semi-Calabi-Yau orbifolds and mirror pairs

TL;DR

This paper extends cohomological mirror duality to higher dimensions and multiple factors, using Berglund-Hübsch duality and Landau-Ginzburg/Calabi-Yau correspondence, including non-Calabi-Yau fixed loci.

Contribution

It generalizes mirror duality to broader classes of orbifolds and fixed loci, beyond traditional Calabi-Yau cases, through a novel proof technique.

Findings

Mirror duality applies to fixed loci of involutions beyond Calabi-Yau categories.

The method encompasses all examples constructed via Berglund-Hübsch duality.

Includes hypersurfaces of general type in the duality framework.

Abstract

We generalize the cohomological mirror duality of Borcea and Voisin in any dimension and for any number of factors. Our proof applies to all examples which can be constructed through Berglund-H\"{u}bsch duality. Our method is a variant of the so-called Landau-Ginzburg/Calabi-Yau correspondence of Calabi-Yau orbifolds with an involution that does not preserve the volume form. We deduce a version of mirror duality for the fixed loci of the involution, which are beyond the Calabi-Yau category and feature hypersurfaces of general type.