Completed volumes and the DR-cycle

Martin Möller; Miguel Prado

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arXiv · 2605.27611

Completed volumes and the DR-cycle

Martin Möller·Miguel Prado

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Abstract

We show that the completed volumes introduced by Duriev-Goujard-Yakovlev as an approximation to compute Masur-Veech volumes via Witten-Kontsevich's combinatorial classes agrees with the top intersection of the tautological class on the double ramification cycle, computable as a coefficient of a Chiodo class. For the proof we describe the components of the double ramification cycle and their excess intersection classes to the extent seen by the top tautological intersection. This gives a recursion computing completed volumes in terms of volumes appearing in a certain set of level graphs, not only for quadratic differentials. It also completes the work of Duriev-Goujard-Yakovlev solving the technically most involved case of strata with two singularities.

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Martin Möller, Miguel Prado. 2026-05-26. Completed volumes and the DR-cycle. https://arxiv.org/abs/2605.27611

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