Hodge-Lyubeznik numbers
Algebraic Geometry
2025-06-24 v3
Abstract
We define a Hodge-theoretical refinement of the Lyubeznik numbers for local rings of complex algebraic varieties. We prove that these numbers are independent of the choices made in their definition and that, for the local ring of an isolated singularity, they can be expressed in terms of the Hodge numbers of the cohomology of the link of the singularity. We give examples of isolated singularities with the same Lyubeznik numbers but different Hodge-Lyubeznik numbers.
Cite
@article{arxiv.2407.10010,
title = {Hodge-Lyubeznik numbers},
author = {Ricardo Garcia Lopez and Claude Sabbah},
journal= {arXiv preprint arXiv:2407.10010},
year = {2025}
}
Comments
V2: Final version, a few signs and typos corrected, Example 1 on p. 7 and Remark (a) on p. 8 added. V3: Post-publication version correcting a missing Tate twist, thanks to Bradley Dirks. A corrigendum will be published in Comptes Rendus