Illinois Journal of Mathematics

Borcea–Voisin mirror symmetry for Landau–Ginzburg models

Amanda Francis, Nathan Priddis, and Andrew Schaug

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Fan–Jarvis–Ruan–Witten theory is a formulation of physical Landau–Ginzburg models with a rich algebraic structure, rooted in enumerative geometry. As a consequence of a major physical conjecture, called the Landau–Ginzburg/Calabi–Yau correspondence, several birational morphisms of Calabi–Yau orbifolds should correspond to isomorphisms in Fan–Jarvis–Ruan–Witten theory. In this paper, we exhibit some of these isomorphisms that are related to Borcea–Voisin mirror symmetry. In particular, we develop a modified version of Berglund–Hübsch–Krawitz mirror symmetry for certain Landau–Ginzburg models. Using these isomorphisms, we prove several interesting consequences in the corresponding geometries.

Article information

Illinois J. Math., Volume 63, Number 3 (2019), 425-461.

Received: 30 April 2019
Revised: 2 July 2019
First available in Project Euclid: 19 September 2019

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Zentralblatt MATH identifier

Primary: 14J32: Calabi-Yau manifolds
Secondary: 14J33: Mirror symmetry [See also 11G42, 53D37] 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45] 14J28: $K3$ surfaces and Enriques surfaces 51P05: Geometry and physics (should also be assigned at least one other classification number from Sections 70-86)


Francis, Amanda; Priddis, Nathan; Schaug, Andrew. Borcea–Voisin mirror symmetry for Landau–Ginzburg models. Illinois J. Math. 63 (2019), no. 3, 425--461. doi:10.1215/00192082-7899497.

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