Editing Meromorphic function (section)

===Higher dimensions===
In [[several complex variables]], a meromorphic function is defined to be locally a quotient of two holomorphic functions. For example, <math>f(z_1, z_2) = z_1 / z_2</math> is a meromorphic function on the two-dimensional complex affine space. Here it is no longer true that every meromorphic function can be regarded as a holomorphic function with values in the [[Riemann sphere]]: There is a set of "indeterminacy" of [[codimension]] two (in the given example this set consists of the origin <math>(0, 0)</math>).

Unlike in dimension one, in higher dimensions there do exist compact [[complex manifold]]s on which there are no non-constant meromorphic functions, for example, most [[complex torus|complex tori]].