Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Szeg\"o Kernel on a Sewn Riemann Surface   We describe the Szeg\"o kernel on a higher genus Riemann surface in terms of
Szeg\"o kernel data coming from lower genus surfaces via two explicit sewing
procedures where either two Riemann surfaces are sewn together or a handle is
sewn to a Riemann surface. We consider in detail the examples of the Szeg\"o
kernel on a genus two Riemann surface formed by either sewing together two
punctured tori or by sewing a twice-punctured torus to itself. We also consider
the modular properties of the Szeg\"o kernel in these cases.

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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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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: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: econ