  In this paper we study the supersingular locus of the reduction modulo p of
the Shimura variety for GU(1,s) in the case of an inert prime p. Using
Dieudonn\'e theory we define a stratification of the corresponding moduli space
of p-divisible groups. We describe the incidence relation of this
stratification in terms of the Bruhat-Tits building of a unitary group.
  In the case of GU(1,2), we show that the supersingular locus is
equi-dimensional of dimension 1 and is of complete intersection. We give an
explicit description of the irreducible components and their intersection
behaviour.
