Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Seiberg-Witten Monopole Equations And Riemann Surfaces   The twice-dimensionally reduced Seiberg-Witten monopole equations admit
solutions depending on two real parameters (b,c) and an arbitrary analytic
function f(z) determining a solution of Liouville's equation. The U(1) and
manifold curvature 2-forms F and R^1_2 are invariant under fractional SL(2,R)
transformations of f(z). When b=1/2 and c=0 and f(z) is the Fuchsian function
uniformizing an algebraic function whose Riemann surface has genus p \geq 2 ,
the solutions, now SL(2,R) invariant, are the same surfaces accompanied by a
U(1) bundle of c_1=\pm (p-1) and a 1-component constant spinor.

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The categories of this paper are: math
9
The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs