(p, a> The sheaf m Co avw . is a fine sheaf over M , as noted earlier; so this provides part of a fine resolution of the sheaf 61, and raises the question of whether this can be extended further as a fine resolution of 0 .

In this sense, divisors merely furnish a description of the zeros and singularities of meromorphic functions. In the case of a single complex variable, the sheaf an alternative and much simpler description; and this simplicity is one of the distinctive differences between the function theory of one and of several complex variables. 8- is therefore naturally isomorphic to the additive group of the integers. ) To describe the topology of , = 7t/ O* , recall that such a quotient sheaf is always topologized by defining the images of sections of 'YY(* as a basis for the open sets of over a basis of the open sets of M , ' .

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Lectures on Riemann Surfaces (Princeton Mathematical Notes) by Robert C. Gunning

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