Hodge–Lyubeznik numbers

Ricardo García López; Claude Sabbah

doi:10.5802/crmath.724

Hodge–Lyubeznik numbers

Titre traduit de la contribution: Nombres de Hodge–Lyubeznik

Ricardo García López
, Claude Sabbah

University of Barcelona

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

Titre traduit de la contribution	Nombres de Hodge–Lyubeznik
langue originale	Anglais
Pages (de - à)	213-221
Nombre de pages	9
journal	Comptes Rendus Mathematique
Volume	363
Les DOIs	https://doi.org/10.5802/crmath.724
état	Publié - 1 janv. 2025

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10.5802/crmath.724

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title = "Hodge–Lyubeznik numbers",

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.",

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AB - 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.

KW - Hodge numbers

KW - Lyubeznik numbers

KW - mixed Hodge modules

UR - https://www.scopus.com/pages/publications/105003403481

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DO - 10.5802/crmath.724

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AN - SCOPUS:105003403481

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ER -

Hodge–Lyubeznik numbers

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