Hodge numbers of Landau-Ginzburg models. (English) Zbl 1467.14025
Summary: We study the Hodge numbers \(f^{p, q}\) of Landau-Ginzburg models as defined by L. Katzarkov et al. [Proc. Symp. Pure Math. 78, 87–174 (2008; Zbl 1206.14009)]. 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 \(h^{p, q}(X) = f^{3 - q, p}(Y, w)\).
MSC:
| 14C30 | Transcendental methods, Hodge theory (algebro-geometric aspects) |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 14J33 | Mirror symmetry (algebro-geometric aspects) |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
| 32J25 | Transcendental methods of algebraic geometry (complex-analytic aspects) |
| 53D37 | Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category |
Citations:
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