The boundary of a totally geodesic subvariety of moduli space
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915055120941056 |
|---|---|
| author | Benirschke, Frederik Dozier, Benjamin Rached, John |
| author_facet | Benirschke, Frederik Dozier, Benjamin Rached, John |
| contents | We consider subvarieties $N$ of $\mathcal{M}_{g,n}$, the moduli space of genus $g$ Riemann surfaces with $n$ marked points, that are totally geodesic with respect to the Teichmüller metric. The Deligne-Mumford boundary of $\mathcal{M}_{g,n}$ decomposes into strata, each of which is essentially a product of lower complexity moduli spaces -- in such spaces there is a natural notion of totally geodesic. We show that the boundary locus of $N$ in any such stratum is itself totally geodesic. Furthermore, we prove that each such boundary locus decomposes into prime pieces, and for each such piece the projection to each factor is locally isometric in an appropriate sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06765 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The boundary of a totally geodesic subvariety of moduli space Benirschke, Frederik Dozier, Benjamin Rached, John Geometric Topology Algebraic Geometry Dynamical Systems We consider subvarieties $N$ of $\mathcal{M}_{g,n}$, the moduli space of genus $g$ Riemann surfaces with $n$ marked points, that are totally geodesic with respect to the Teichmüller metric. The Deligne-Mumford boundary of $\mathcal{M}_{g,n}$ decomposes into strata, each of which is essentially a product of lower complexity moduli spaces -- in such spaces there is a natural notion of totally geodesic. We show that the boundary locus of $N$ in any such stratum is itself totally geodesic. Furthermore, we prove that each such boundary locus decomposes into prime pieces, and for each such piece the projection to each factor is locally isometric in an appropriate sense. |
| title | The boundary of a totally geodesic subvariety of moduli space |
| topic | Geometric Topology Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2412.06765 |