Uniqueness of the Veech 14-gon

2022/10/18 by Winsor, Karl
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2210.09702

Abstract

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 ΩM₃(2,2).

Related

• Non-existence and finiteness results for Teichmueller curves in Prym loci
• Teichmueller curves generated by Weierstrass Prym eigenforms in genus three and genus four
• Finiteness results for Teichmueller curves
• There are no primitive Teichmüller curves in \Prym(2,2)
• Teichmueller curves in genus three and just likely intersections in G_mⁿ x G_aⁿ