  We establish a close connection between intersection multiplicities of
special cycles on arithmetic models of the Shimura variety for GU(1,2) and
Fourier coefficients of derivatives of certain incoherent Eisenstein series,
confirming a conjecture of Kudla and Rapoport. The paper is divided into two
parts. The first part is the bulk of the paper and investigates intersections
of local special cycles which are defined on a certain moduli space of
p-divisible groups. This moduli space of p-divisible groups can be used for the
uniformization of the completion of the Shimura variety along the supersingular
locus in the fiber at an inert prime p. We investigate the structure of local
special cycles and of their intersections. In particular, we give an explicit
description of the special fiber of a local special cycle. We then prove an
explicit formula for the intersection multiplicity of three local special
cycles and relate it to certain hermitian representation densities, also
confirming a conjecture of Kudla and Rapoport. To this end, we also give an
explicit inductive formula for the relevant hermitian representation densities
\alpha_p(1_s,T), where T is of the form diag(p^{a_1},...,p^{a_n}). In the
second part, we apply the main result of the first part to prove the relation
of intersection multiplicities of (global) special cycles and Fourier
coefficients of derivatives of Eisenstein series.
