  This note is concerned with the scaling limit as N approaches infinity of
n-point correlations between zeros of random holomorphic polynomials of degree
N in m variables. More generally we study correlations between zeros of
holomorphic sections of powers L^N of any positive holomorphic line bundle L
over a compact Kahler manifold. Distances are rescaled so that the average
density of zeros is independent of N. Our main result is that the scaling
limits of the correlation functions and, more generally, of the "correlation
forms" are universal, i.e. independent of the bundle L, manifold M or point on
M.
