Isoperiodic foliation of the stratum $Ω\mathcal{M}_1(1,1,-2)$

Fuente: arXiv
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Autori principali: Faraco, Gianluca, Tahar, Guillaume, Zhang, Yongquan
Natura: Preprint
Pubblicazione: 2023
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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