Form rings and regular sequences

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Abstract
Hironaka, in his paper [H1] on desingularization of algebraic varieties over a field of characteristic 0, to deal with singular points develops the algebraic apparatus of the associated graded ring, introducing standard bases of ideals, numerical characters ν* and τ* etc. Such a point of view involves a deep investigation of the ideal b* generated by the initial forms of the elements of an ideal A of a local ring, with respect to a certain ideal a.