The combinatorial part of the cohomology of a singular variety

2009/02/24 by Donu Arapura, Arapura, Donu, Parsa Bakhtary +3 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.0902.4234

9 pages

arxiv created 2009/02/24 · openalex publication_date 2009/02/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the first step of the weight filtration on the cohomology of a proper complex algebraic variety, which we call the combinatorial part. We obtain a natural upper bound on its size, which gives rather strong information about the topology of rational singularities.

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• Fundamental groups of links of isolated singularities

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• Weights on cohomology, invariants of singularities, and dual complexes
• Weight zero part of the first cohomology of complex algebraic varieties
• Hodge Conjecture via Singular Varieties
• Hodge symmetry and Lefschetz theorems for singular varieties
• Filtrations on combinatorial intersection cohomology and invariants of subdivisions