Volumes of moduli spaces of flat surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866913182556094464 |
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| author | Sauvaget, Adrien |
| author_facet | Sauvaget, Adrien |
| contents | We study the moduli spaces of flat surfaces with prescribed conical singularities. Veech showed that these spaces are diffeomorphic to the moduli spaces of marked Riemann surfaces, and endowed with a natural volume form depending on the orders of the singularities. We show that the volumes of these spaces are finite. Moreover we show that they are explicitely computable by induction on the Euler characteristics of the punctured surface for almost all orders of the singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_03198 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Volumes of moduli spaces of flat surfaces Sauvaget, Adrien Algebraic Geometry Differential Geometry 14H10, 14H51, 14C17, 30F45 We study the moduli spaces of flat surfaces with prescribed conical singularities. Veech showed that these spaces are diffeomorphic to the moduli spaces of marked Riemann surfaces, and endowed with a natural volume form depending on the orders of the singularities. We show that the volumes of these spaces are finite. Moreover we show that they are explicitely computable by induction on the Euler characteristics of the punctured surface for almost all orders of the singularities. |
| title | Volumes of moduli spaces of flat surfaces |
| topic | Algebraic Geometry Differential Geometry 14H10, 14H51, 14C17, 30F45 |
| url | https://arxiv.org/abs/2004.03198 |