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arXiv · 2307.15607

Modularity of Landau-Ginzburg models

Charles Doran·Andrew Harder·Ludmil Katzarkov·Mikhail Ovcharenko·Victor Przyjalkowski
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Abstract

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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Charles Doran, Andrew Harder, Ludmil Katzarkov, Mikhail Ovcharenko, Victor Przyjalkowski. 2023-07-28. Modularity of Landau-Ginzburg models. https://doi.org/10.1134/s008154382501002x

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