Uniqueness of the Veech 14-gon

We obtain the first complete classification result for algebraically primitive Teichmüller curves in a stratum component in genus greater than 2. Specifically, we show that the Veech 14-gon generates the unique algebraically primitive Teichmüller curve in the hyperelliptic component of the stratum $\mathrm{\Omega }{\mathcal{M}}_3(2,2)$.