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Dual fans and mirror symmetry. (English) Zbl 1375.14133
Summary: We show that the mirror constructions of Greene-Plesser, Berglund-Hübsch, Batyrev, Batyrev-Borisov, Givental and Hori-Vafa can be expressed in terms of what we call dual fans. To do this, we associate to a pair of dual fans a pair of toric Landau-Ginzburg models, and we describe a process by which each of the mirror constructions listed also produces a pair of toric Landau-Ginzburg models. Replacing mirror pairs by toric Landau-Ginzburg models is reversible, and our main result is that the dual fan models and the mirror pairs models coincide.

MSC:
14J33 Mirror symmetry (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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