Pure homology of algebraic varieties

2003/02/27 by Andrzej Weber, Weber, Andrzej · 1 citation
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Algebraic variety #Biology #Cellular homology #Cohomology #Commutative Algebra and Its Applications #Gene #Genetics #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Intersection homology #Invariant (physics) #Mathematical analysis #Mathematics #Mayer–Vietoris sequence #Pure mathematics #Relative homology #Singular homology #math.AG #math.AT

paper · pdf · doi:10.48550/arxiv.math/0302340

Key words: Algebraic varieties, weight filtration, intersection homology. 12 pages. Final version. To appear in Topology

openalex publication_date 2003/02/27 · arxiv created 2003/09/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that for a complete complex algebraic variety the pure component of homology coincides with the image of intersection homology. Therefore pure homology is topologically invariant. To obtain slightly more general results we introduce "image homology" for noncomplete varieties.

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