Higher Dimensions
In several complex variables, a meromorphic function is defined to be locally a quotient of two holomorphic functions. For example, 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 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 ).
Unlike in dimension one, in higher dimensions there do exist complex manifolds on which there are no non-constant meromorphic functions, for example, most complex tori.
Read more about this topic: Meromorphic Function
Famous quotes containing the words higher and/or dimensions:
“The higher a man stands, the more the word “vulgar” becomes unintelligible to him.”
—John Ruskin (1819–1900)
“I was surprised by Joe’s asking me how far it was to the Moosehorn. He was pretty well acquainted with this stream, but he had noticed that I was curious about distances, and had several maps. He and Indians generally, with whom I have talked, are not able to describe dimensions or distances in our measures with any accuracy. He could tell, perhaps, at what time we should arrive, but not how far it was.”
—Henry David Thoreau (1817–1862)