Hodge-Lyubeznik numbers
Ricardo Garcia Lopez, Claude Sabbah

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · advanced mathematical theories
