Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The infinitesimal multiplicities and orientations of the blow-up set of
  the Seiberg-Witten equation with multiple spinors   I construct multiplicies and orientations of tangent cones to any blow-up set
$Z$ for the Seiberg-Witten equation with multiple spinors. This is used to
prove that $Z$ determines a homology class, which is shown to be equal to the
Poincar\'{e} dual of the first Chern class of the determinant line bundle. I
also obtain a lower bound for the 1-dimensional Hausdorff measure of $Z$.

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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio