Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial resolution by toroidal blow-ups   We answer a question of Keel: How much can one improve a non-toroidal ideal
sheaf by a sequence of toroidal blow-ups? Version2: Corollary 5 was proved
earlier by Tevelev and Ulirsch.

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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ