Abstract
We study the Hodge numbers fp,q 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,w) so that hp,q(X)=f3−q,p(Y,w).
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