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arXiv · 1603.05151

A calculus for the moduli space of curves

R. Pandharipande
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Abstract

This article accompanies my lecture at the 2015 AMS summer institute in algebraic geometry in Salt Lake City. I survey the recent advances in the study of tautological classes on the moduli spaces of curves. After discussing the Faber-Zagier relations on the moduli spaces of nonsingular curves and the kappa rings of the moduli spaces of curves of compact type, I present Pixton's proposal for a complete calculus of tautological classes on the moduli spaces of stable curves. Several open questions are discussed. An effort has been made to condense a great deal of mathematics into as few pages as possible with the hope that the reader will follow through to the end.

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R. Pandharipande. 2016-03-16. A calculus for the moduli space of curves. https://arxiv.org/abs/1603.05151

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