Completed volumes and the DR-cycle
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.
Cite
@article{arxiv.2605.27611,
title = {Completed volumes and the DR-cycle},
author = {Martin Möller and Miguel Prado},
journal= {arXiv preprint arXiv:2605.27611},
year = {2026}
}