Weight zero part of the first cohomology of complex algebraic varieties

Morihiko Saito

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arXiv · 1804.03632

Weight zero part of the first cohomology of complex algebraic varieties

Morihiko Saito

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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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Morihiko Saito. 2018-04-10. Weight zero part of the first cohomology of complex algebraic varieties. https://arxiv.org/abs/1804.03632

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