Papers › Modularity of Landau-Ginzburg models
Modularity of Landau-Ginzburg models
Charles Doran, Andrew Harder, Ludmil Katzarkov, Mikhail Ovcharenko, Victor Przyjalkowski
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For each Fano threefold, we construct a family of Landau-Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry; they are log Calabi-Yau varieties with proper potential maps; they admit open algebraic torus charts on which the potential function w restricts to a Laurent polynomial satisfying a deformation of the Minkowski ansatz; the general fibres of w are Dolgachev-Nikulin dual to the anticanonical hypersurfaces in X. To do this, we study the deformation theory of Landau-Ginzburg models in arbitrary dimension, following the third-named author, Kontsevich, and Pantev, specializing to the case of Landau-Ginzburg models obtained from Laurent polynomials. Our proof of Dolgachev-Nikulin mirror symmetry is by detailed case-by-case analysis, refining work of Cheltsov and the fifth-named author.
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