Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Gorenstein conjecture fails for the tautological ring of
  $\mathcal{\bar M}_{2,n}$   Let $N$ be the smallest integer such that there is a non-tautological
cohomology class of even degree on $\mathcal{\bar M}_{2,N}$. We remark that
there is such a non-tautological class on $\mathcal{\bar M}_{2,20}$, by work of
Graber and Pandharipande. We show that $\mathcal{\bar M}_{2,N}$ has
non-tautological cohomology only in one degree, which is not the middle degree.
In particular, it follows that the tautological ring of $\mathcal{\bar
M}_{2,N}$ is not Gorenstein. We present some evidence suggesting that N=20
holds.

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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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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: chem-ph