Weight zero part of the first cohomology of complex algebraic varieties

2018/04/10 by Morihiko Saito, Saito, Morihiko · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1804.03632

openalex publication_date 2018/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the weight 0 part of the first cohomology of a complex algebraic variety X is a topological invariant, and give an explicit description of its dimension using a topological construction of the normalization of X, where X can be reducible, but must be equidimensional. The first assertion is known in the X compact case by A. Weber, where intersection cohomology is used. Note that the weight 1 or 2 part of the first cohomology is not a topological (or even analytic) invariant in the non-compact case by Serre's example.

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