Isoperiodic foliation of the stratum $Ω\mathcal{M}_1(1,1,-2)$
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914175077318656 |
|---|---|
| author | Faraco, Gianluca Tahar, Guillaume Zhang, Yongquan |
| author_facet | Faraco, Gianluca Tahar, Guillaume Zhang, Yongquan |
| contents | This paper describes the geometry and topology of leaves of the isoperiodic foliation of the stratum $Ω\mathcal{M}_1(1,1,-2)$. We prove that each leaf is a surface of infinite genus homeomorphic to the Loch Ness monster surface and supports a singular Euclidean structure whose singularities correspond to isoperiodic forms in the lower stratum $Ω\mathcal{M}_1(2,-2)$. Along the way we also characterize the possible groups arising as the Veech group of a leaf and give a description of the large-scale conformal geometry of the wall-and-chamber decomposition of the leaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06761 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Isoperiodic foliation of the stratum $Ω\mathcal{M}_1(1,1,-2)$ Faraco, Gianluca Tahar, Guillaume Zhang, Yongquan Geometric Topology Algebraic Geometry Dynamical Systems This paper describes the geometry and topology of leaves of the isoperiodic foliation of the stratum $Ω\mathcal{M}_1(1,1,-2)$. We prove that each leaf is a surface of infinite genus homeomorphic to the Loch Ness monster surface and supports a singular Euclidean structure whose singularities correspond to isoperiodic forms in the lower stratum $Ω\mathcal{M}_1(2,-2)$. Along the way we also characterize the possible groups arising as the Veech group of a leaf and give a description of the large-scale conformal geometry of the wall-and-chamber decomposition of the leaves. |
| title | Isoperiodic foliation of the stratum $Ω\mathcal{M}_1(1,1,-2)$ |
| topic | Geometric Topology Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2305.06761 |