Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative Canonical Sheaves of a Family of Curves   In this paper we show that the relative canonical sheaf of a relatively
minimal fibration of curves over a curve is semi-ample ; in fact, its
m-tensored product is base point free for any m > 1. We use Koszul cohomology
with it to prove that the relative canonical ring of the fibration is generated
in degree up to five.

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The categories of this paper are: hep-ph
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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: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas