Year: 2026
Type: preprint
Abstract: 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 $(U,f)$, where $U$ is a smooth quasi-projective complex variety and $f$ is a regular function on $U$. Under a natural non-degeneracy assumption, we show that the classes of such models in the localized Grothendieck ring of complex algebraic varieties with exponentials are invariant under crepant birational equivalences. Consequently, the irregular Hodge numbers of the twisted de Rham cohomology $\mathrm{H}^k_{\mathrm{dR}}(U,f)$ are invariant as well.
Source: arXiv (Cornell University)
Author: Qin, Yichen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7168353015