On the invariance of irregular Hodge numbers under crepant birational equivalences

The Batyrev–Kontsevich theorem asserts that birational Calabi–Yau varieties have the same Hodge numbers. In this article, we prove an analogue for Landau–Ginzburg models $(U,f)$, consisting of smooth quasi-projective complex varieties $U$ with regular functions $f$ on $U$. We show that the irregular Hodge numbers of the twisted de Rham cohomology ${\mathrm{H}}_{\mathrm{d}\mathrm{R}}^k(U,f)$ are invariant under crepant birational equivalences.