Key points are not available for this paper at this time.
At present a great deal is known about the value distribution of systems of meromorphic functions on an open Riemann surface. One has the beautiful results of Picard, E. Borel, Nevanlinna, Ahlfors, H. and J. Weyl and many others to point to. (See 1, 2.) The aim of this paper is to make the initial step towards an n-dimensional analogue of this theory. A natural general setting for the value distribution theory is the following one. We consider a complex n-manifold X and a holomorphic vector bundle E over X whose fiber dimension equals the dimension of X and wish to study the zero-sets of holomorphic sections of E. When X is compact (and without boundary) then it is well-known that if the zeroes of any continuous section are counted properly then the algebraic sum of these zero-points is independent of the section and is given by the integral of the nth Chern(2) class of E over X: Thus we have zeroes of s = | cn(E), (1.1) Number of J x
Bott et al. (Fri,) studied this question.