  The diffusion approximation of the Wright-Fisher model of population genetics
leads to partial differentiable equations, the so-called Kolmogorov equations,
with an operator that degenerates at the boundary. Standard tools do not apply,
and in fact, solutions lack regularity properties. In this paper, we develop a
regularising blow-up scheme for a certain class of solutions of the backward
Kolmogorov equation, the iteratively extended global solutions presented in
\cite{THJ5}, and establish their uniqueness. As the model describes the random
genetic drift of several alleles at the same locus from a backward perspective,
the singularities result from the loss of an allele. While in an analytical
approach, this causes substantial difficulties, from a biological or geometric
perspective, this is a natural process that can be analyzed in detail. The
presented scheme regularises the solution via a tailored successive
transformation of the domain.
