2015/09/30 by A Chiodo, Alessandro Chiodo, Elana Kalashnikov +1
Mathematics · Physics and Astronomy · Psychology · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Calabi–Yau manifold #Dimension (graph theory) #Duality (order theory) #Geometry and complex manifolds #Involution (esoterism) #Mathematics #Psychology #Pure mathematics #hep-th #math.AG
paper · pdf · doi:10.1016/j.aim.2020.106998
published as Adv. Math. 363 (2020), 106998, 46 pp · 35 pages, 2 figures. V2 Major revision, main theorem generalized and relation to orbifold cohomology given in dimension two. V3 Revised section 4 and proof of last theorem. V4 minor corrections. To appear in Adv. Math
arxiv created 2020/01/10 · openalex publication_date 2020/01/24 · arxiv updated 2022/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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-Hübsch 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.