An extraordinary origami curve

Description:

This origami curve is defined by an origami W consisting of 8 squares.

Properties:

• genus of W: 3
• stratum: 4 zeroes
• The Veech group is SL_2(Z) and the origami is characteristic
• The Jacobian of the associated family of curves has a two dimensional fixed part
• It is the only non-trivial Teichmueller curve that is in the same time a Shimura curve
• The corresponding Teichmueller curve is intersected by infinitely many other Teichmueller curves all defined by origamis

References:

• An extraordinary origami curve, Herrlich/Schmithuesen. Preprint 2005. http://xxx.uni-augsburg.de/abs/math.AG/0509195
• Shimura- and Teichmueller curves, Moeller. Preprint 2005. http://xxx.uni-augsburg.de/abs/math.AG/0501333

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