PreprintarXiv licencearXiv
On the invariance of irregular Hodge numbers under crepant birational equivalences
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 HkdR(U,f) are invariant as well.
Related
- Stringy Irregular Hodge Numbers for Non-Simplicial Toric Landau--Ginzburg Data
- Connected irregular cospectral graphs with distinct Lovász numbers
- Du Bois cohomology of noncommutative spaces and the Hodge numbers invariance conjecture for singular varieties
- Hirzebruch signature theorem on Hochschild homology, with applications to derived invariance of Hodge numbers
- Crepant partial resolutions of the nilpotent cone via Hamiltonian reduction
BibTeX
@misc{qin2026invariance,
title = {{On the invariance of irregular Hodge numbers under crepant birational equivalences}},
author = {Yichen Qin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.12531},
eprint = {2607.12531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.12531},
}
RIS
TY - UNPB
TI - On the invariance of irregular Hodge numbers under crepant birational equivalences
AU - Yichen Qin
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2607.12531
UR - https://arxiv.org/abs/2607.12531
AB - 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 H^k_dR(U,f) are invariant as well.
ER -