Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincar\'e duality of wonderful compactifications and tautological rings   Let $g \geq 2$. Let $M_{g,n}^{rt}$ be the moduli space of $n$-pointed genus
$g$ curves with rational tails. Let $C_g^n$ be the $n$-fold fibered power of
the universal curve over $M_g$. We prove that the tautological ring of
$M_{g,n}^{rt}$ has Poincar\'e duality if and only if the same holds for the
tautological ring of $C_g^n$. We also obtain a presentation of the tautological
ring of $M_{g,n}^{rt}$ as an algebra over the tautological ring of $C_g^n$.
This proves a conjecture of Tavakol. Our results are valid in the more general
setting of wonderful compactifications.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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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: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph