Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weight zero part of the first cohomology of complex algebraic varieties   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.

20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg