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arXiv · 1904.07520

An action of the Polishchuk differential operator via punctured surfaces

Gabriel C. Drummond-Cole·Mehdi Tavakol
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Abstract

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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Gabriel C. Drummond-Cole, Mehdi Tavakol. 2019-04-16. An action of the Polishchuk differential operator via punctured surfaces. https://arxiv.org/abs/1904.07520

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