  In this article we compute the mass associated to any unimodular lattice in a
Hermitian space over an arbitrary CM field under a condition at 2. We study the
geometry and arithmetic of the basic locus of the GU(r,s)-Shimura variety
associated to an imaginary quadratic field modulo a good prime p>2. We give
explicit formulas for the numbers of irreducible and connected components of
the basic locus, and of points of the zero-dimensional Ekedahl-Oort (EO)
stratum, as well as of the irreducible components of basic EO strata when the
signature is either (1, n-1) or (2,2).
