Flat surfaces with the floorplan of gothic cathedrals define an exceptional series of
Teichmüller curves. We give an overview of the ways to define Teichmüller curves
using Hilbert modular forms of non-parallel weight and the flat surfaces invariants
that can be computed from this viewpoint.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/7239