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Hori-Vafa mirror models for complete intersections in weighted projective spaces and weak Landau-Ginzburg models. (English) Zbl 1236.14038
In an earlier work [Commun. Number Theory Phys. 1, No. 4, 713–728 (2008; Zbl 1194.14065)], the author conjectured that any smooth Fano variety of dimension \(N\) with Picard rank 1 has a weak Landau-Ginzburg model \(f\in \mathbb{C}[x_{1}^{\pm 1},\dots, x_{N}^{\pm 1}]\). This conjecture holds, for instance, for threefolds and complete intersections in projective spaces. In this work, the author proves that the conjecture holds for smooth complete intersections of Cartier divisors in weighted projective spaces. In other words, the author shows that Hori-Vafa suggestions for Landau-Ginzburg models for such varieties may be interpreted as Laurent polynomials.

MSC:
14J33 Mirror symmetry (algebro-geometric aspects)
14M10 Complete intersections
14Q15 Computational aspects of higher-dimensional varieties
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