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On Landau-Ginzburg models for Fano varieties. (English) Zbl 1194.14065
Mirror symmetry was originally formulated for Calabi-Yau manifolds and was later generalized to Fano varieties. A mirror to a Fano variety $$X$$ is a Landau-Ginzburg model, a non-compact complex manifold $$M$$ with a complex-valued function $$f$$ on it, called the superpotential. The paper under review discusses a general strategy for finding mirrors to Fano threefolds, providing explicit answers for threefolds with Picard group $$\mathbb{Z}$$ of genera $$9$$, $$10$$ and $$12$$.

MSC:
 14J45 Fano varieties
Keywords:
mirror symmetry; Fano varieties
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