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arXiv · 1708.01174

Hodge numbers of Landau-Ginzburg models

Andrew Harder
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Abstract

We study the Hodge numbers of Landau-Ginzburg models as defined by Katzarkov, Kontsevich and Pantev. First we show that these numbers can be computed using ordinary mixed Hodge theory, then we give a concrete recipe for computing these numbers for the Landau-Ginzburg mirrors of Fano threefolds. We finish by proving that for a crepant resolution of a Gorenstein toric Fano threefold $X$ there is a natural LG mirror $(Y,\mathsf{w})$ so that $h^{p,q}(X) = f^{3-q,p}(Y,\mathsf{w})$.

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Andrew Harder. 2017-08-03. Hodge numbers of Landau-Ginzburg models. https://arxiv.org/abs/1708.01174

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