  We study "straight equisingular deformations", a linear subfunctor of all
equisingular deformations and describe their seminuniversal deformation by an
ideal containing the fixed Tjurina ideal. Moreover, we show that the base space
of the seminuniversal straight equisingular deformation appears as the fibre of
a morphism from the {\mu}-constant stratum onto a punctual Hilbert scheme
parametrizing certain zero-dimensional schemes concentrated in the singular
point. Although equisingular deformations of plane curve singularities are very
well understood, we believe that this aspect may give a new insight in their
inner structure.

Algebraic Geometry