Torus branched coverings

A surface S is said to be a torus branched covering if there exists a flat branched covering from S to a flat torus.

Such surfaces have a simple J-invariant, but are not the only ones (see for example TwoDirectionsSurface).

Such a surface is a Veech surface (arithmetic surfaces) if and only if the covering can be choosen such that there is only one ramification point.

References

• http://poincare.math.indiana.edu/~cjudge/research/papers/affinemaps.pdf
• http://arxiv.org/abs/math/0107204