Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zariski's conjecture and Euler-Chow series   We study the relations between the finite generation of Cox ring, the
rationality of Euler-Chow series and Poincar\'e series and Zariski's conjecture
on dimensions of linear systems. We prove that if the Cox ring of a smooth
projective variety is finitely generated, then all Poincar\'e series of the
variety are rational. We also prove that the multi-variable Poincar\'e series
associated to big divisors on a smooth projective surface are rational,
assuming the rationality of multi-variable Poincare series on curves.

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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: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: econ