Complete classification of algebraically primitive Teichmüller curves in $Ω\mathcal{M}_g(g-1,g-1)^{\mathrm{hyp}}$

Abstract

We give a complete classification of algebraically primitive Teichmüller curves in $Ω\mathcal M_g(g-1,g-1)^{\mathrm{hyp}}$ for $g>2$. These curves are precisely those generated by the Veech $2p$-gons, where $p=2g+1$ is prime.