Hodge–Lyubeznik numbers

Ricardo García López; Claude Sabbah

doi:10.5802/crmath.724

Hodge–Lyubeznik numbers

Ricardo García López
, Claude Sabbah

University of Barcelona

Research output: Contribution to journal › Article › peer-review

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.

Translated title of the contribution	Nombres de Hodge–Lyubeznik
Original language	English
Pages (from-to)	213-221
Number of pages	9
Journal	Comptes Rendus Mathematique
Volume	363
DOIs	https://doi.org/10.5802/crmath.724
Publication status	Published - 1 Jan 2025

Keywords

Hodge numbers
Lyubeznik numbers
mixed Hodge modules

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10.5802/crmath.724

Cite this

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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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year = "2025",

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doi = "10.5802/crmath.724",

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AU - Sabbah, Claude

PY - 2025/1/1

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N2 - 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.

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

U2 - 10.5802/crmath.724

DO - 10.5802/crmath.724

M3 - Article

AN - SCOPUS:105003403481

SN - 1631-073X

VL - 363

SP - 213

EP - 221

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

ER -

Hodge–Lyubeznik numbers

Abstract

Keywords

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