A flat perspective on moduli spaces of hyperbolic surfaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914800599040000 |
|---|---|
| author | Sauvaget, Adrien |
| author_facet | Sauvaget, Adrien |
| contents | Volumes of moduli spaces of hyperbolic cone surfaces were previously defined and computed when the angles of the cone singularities are at most 2pi. We propose a general definition of these volumes without restriction on the angles. This construction is based on flat geometry as our proposed volume is a limit of Masur-Veech volumes of moduli spaces of multi-differentials. This idea generalizes the observation in quantum gravity that the Jackiw-Teitelboim partition function is a limit of minimal string partition functions from Liouville gravity. Finally, we use the properties of these volumes to recover Mirzakhani's recursion formula for Weil-Petersson polynomials. This provides a new proof of Witten-Kontsevich's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A flat perspective on moduli spaces of hyperbolic surfaces Sauvaget, Adrien Algebraic Geometry Mathematical Physics Dynamical Systems Volumes of moduli spaces of hyperbolic cone surfaces were previously defined and computed when the angles of the cone singularities are at most 2pi. We propose a general definition of these volumes without restriction on the angles. This construction is based on flat geometry as our proposed volume is a limit of Masur-Veech volumes of moduli spaces of multi-differentials. This idea generalizes the observation in quantum gravity that the Jackiw-Teitelboim partition function is a limit of minimal string partition functions from Liouville gravity. Finally, we use the properties of these volumes to recover Mirzakhani's recursion formula for Weil-Petersson polynomials. This provides a new proof of Witten-Kontsevich's theorem. |
| title | A flat perspective on moduli spaces of hyperbolic surfaces |
| topic | Algebraic Geometry Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2405.10869 |