  We discuss to what extent the local techniques of resolution of singularities
over fields of characteristic zero can be applied to improve singularities in
general. For certain interesting classes of singularities, this leads to an
embedded resolution via blowing ups in regular centers. We illustrate this for
generic determinantal varieties. The article is partially expository and is
addressed to non-experts who aim to construct resolutions for other special
classes of singularities in positive or mixed characteristic.
