Teichmüller curves in hyperelliptic components of meromorphic strata

Abstract

We provide a complete classification of Teichmüller curves occurring in hyperelliptic components of the meromorphic strata of differentials. Using a non-existence criterion based on how Teichmüller 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.

Includes the appendix: An $\mathbb{R}$-linear non-algebraic manifold by Benjamin Bakker and Scott Mullane. 22 pages, 8 figures