Veech groups and polygonal coverings (Q1580292)

The paper discusses branch points of affine coverings and their effects on Veech groups. It shows that even if one polygon tiles another, the respective Veech groups are not necessarily commensurable and there is no universal bound on the number of the Teichmüller disks passing through the same point of Teichmuller space and having incommensurable lattices Veech groups.