A tale of two volumes of moduli spaces: Weil-Petersson and Masur-Veech
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915842718957568 |
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| author | Chen, Dawei Mullane, Scott |
| author_facet | Chen, Dawei Mullane, Scott |
| contents | Weil-Petersson and Masur-Veech volumes measure the sizes of moduli spaces of Riemann surfaces equipped with hyperbolic and flat metrics, respectively. Over the past several decades, the computation of these volumes has inspired remarkable developments in combinatorial enumeration, intersection theory, and recursion relations. In this survey, we review key results, methods, open problems, as well as interesting parallels that emerge in the approaches to computing both types of volumes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07318 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A tale of two volumes of moduli spaces: Weil-Petersson and Masur-Veech Chen, Dawei Mullane, Scott Geometric Topology Mathematical Physics Algebraic Geometry Combinatorics Metric Geometry Weil-Petersson and Masur-Veech volumes measure the sizes of moduli spaces of Riemann surfaces equipped with hyperbolic and flat metrics, respectively. Over the past several decades, the computation of these volumes has inspired remarkable developments in combinatorial enumeration, intersection theory, and recursion relations. In this survey, we review key results, methods, open problems, as well as interesting parallels that emerge in the approaches to computing both types of volumes. |
| title | A tale of two volumes of moduli spaces: Weil-Petersson and Masur-Veech |
| topic | Geometric Topology Mathematical Physics Algebraic Geometry Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2603.07318 |