Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert-Mumford criterion for nodal curves   We prove by Hilbert-Mumford criterion that a slope stable polarized weighted
pointed nodal curve is Chow asymptotic stable. This generalizes the result of
Caporaso on stability of polarized nodal curves, and of Hasset on weighted
pointed stable curves polarized by the weighted dualizing sheaves. It also
solved a question raised by Mumford and Gieseker to prove the Chow asymptotic
stability of stable nodal curves by Hilbert-Mumford criterion.

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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int