Hodge-Lyubeznik numbers

TL;DR

This paper introduces Hodge-Lyubeznik numbers as a refined invariant for local rings of complex algebraic varieties, demonstrating their independence from choices and their relation to Hodge numbers in isolated singularities.

Contribution

It defines Hodge-Lyubeznik numbers, proves their invariance, and relates them to Hodge numbers for isolated singularities, providing new insights into singularity invariants.

Findings

Hodge-Lyubeznik numbers are independent of definition choices

They can be expressed via Hodge numbers for isolated singularities

Examples show differences from Lyubeznik numbers in some cases

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.