Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 63, Number 3 (2019), 425-461.
Borcea–Voisin mirror symmetry for Landau–Ginzburg models
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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.ijm/1568858866