Teichm\"uller curves in hyperelliptic components of meromorphic strata
Algebraic Geometry
2025-06-25 v1 Dynamical Systems
Geometric Topology
Abstract
We provide a complete classification of Teichm\"uller curves occurring in hyperelliptic components of the meromorphic strata of differentials. Using a non-existence criterion based on how Teichm\"uller curves intersect the boundary of the moduli space we derive a contradiction to the algebraicity of any candidate outside of Hurwitz covers of strata with projective dimension one and Hurwitz covers of zero residue loci in strata with projective dimension two.
Keywords
Cite
@article{arxiv.2305.03309,
title = {Teichm\"uller curves in hyperelliptic components of meromorphic strata},
author = {Martin Möller and Scott Mullane},
journal= {arXiv preprint arXiv:2305.03309},
year = {2025}
}
Comments
Includes the appendix: An $\mathbb{R}$-linear non-algebraic manifold by Benjamin Bakker and Scott Mullane. 22 pages, 8 figures