Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An action of the Polishchuk differential operator via punctured surfaces   For a family of Jacobians of smooth pointed curves there is a notion of
tautological algebra. There is an action of $\mathfrak{sl}_2$ on this algebra.
We define and study a lifting of the Polishchuk operator, corresponding to
$f\in \mathfrak{sl}_2$, on an algebra consisting of punctured Riemann surfaces.
As an application we prove that a collection of tautological relations on
moduli of curves, discovered by Faber and Zagier, come from a class of
relations on the universal Jacobian.

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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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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: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph