Characterizations of lattice surfaces (Q967634)

It is shown that the lattice property for flat surfaces is equivalent to the existence of a positive lower bound for the area of affine triangles in the surface. The set of affine equivalence classes of lattice surfaces for which the area of triangles is bounded by a fixed positive lower bound is shown to be finite, and explicit bounds for its cardinality are derived. Several further characterizations of the lattice property of flat surfaces are given.