The squared snake surface
Description of the surface
The opposite vertical lines are identified by horizontal translation, the vertical lines with the same style are identified.
Basic facts
- genus : 3
- stratum : H(1,1,1,1)
- Veech group :
Some Properties
Indeed, the coloring of the picture above allows us to see how to construct a covering
from S to R^2/Z^2 of degree 2, branched at the points A=(0,0), B=(1/2,0), C=(0,1/2), D=(1/2,1/2). The singularities of S are located at the preimages of those four points.
The
FiniteBlockingProperty in the square says that three points in {A,B,C,D} block every geodesic from the fourth point to itself. Hence, by lifting, every geodesic from the singularity
to itself in S has to meet one of the other singularities
, and by symmetry it works for the three other singularities.
To be written...
References
This surface was introduced in
http://front.math.ucdavis.edu/math.DS/0406510 (page 9)
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