  This article finds a structure of singular sets on compact Kahler surfaces,
which Taubes introduced in the studies of the asymptotic analysis of solutions
to the Kapustin-Witten equations and the Vafa-Witten ones originally on smooth
four-manifolds. These equations can be seen as real four-dimensional analogues
of the Hitchin equations on Riemann surfaces, and one of common obstacles to be
overcome is a certain unboundedness of solutions to these equations, especially
of the "Higgs fields". The singular sets by Taubes describe part of the
limiting behaviour of a sequence of solutions with this unboundedness property,
and Taubes proved that the real two-dimensional Haussdorff measures of these
singular sets are finite. In this article, we look into the singular sets, when
the underlying manifold is a compact Kahler surface, and find out that they
have the structure of an analytic subvariety in this case.
