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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2605.27611 |
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| _version_ | 1866913165717012480 |
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| author | Möller, Martin Prado, Miguel |
| author_facet | Möller, Martin Prado, Miguel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27611 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Completed volumes and the DR-cycle Möller, Martin Prado, Miguel Algebraic Geometry Dynamical Systems Geometric Topology 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. |
| title | Completed volumes and the DR-cycle |
| topic | Algebraic Geometry Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2605.27611 |