A new proof of desingularization over fields of characteristic zero.
We present a proof of embedded desingularization for closed subschemes which does not make use of Hilbert-Samuel function and avoids Hironaka's notion of normal flatness (see also [171 page 224). Given a subscheme defined by equations, we prove that embedded desingularization can be achieved by a sequence of monoidal transformations; where the law of transformation on the equations defining the subscheme is simpler then that used in Hironaka 's procedure. This is done by showing that desingularization...