In particular he computed their multiplicities also in terms of the number of independent meromorphic functions associated to "D" (Riemann-Kempf singularity theorem). More precisely, Kempf mapped "J" locally near "p" to a family of matrices coming from an exact sequence which computes "h"0(O("D")), in such a way that "W""k" corresponds to the locus of matrices of less than maximal rank. The multiplicity then agrees with that of the point on the corresponding rank locus. Explicitly, if  the multiplicity of "W""k" at class("D") is the binomial coefficient  When "k" = "g" − 1, this is "r" + 1, Riemann's formula.