On the use of naturality in algorithmic resolution
the author shows in a very synthetic manner some results concerning algorithmic resolution in characteristic zero (in the sense of \textit{S. Encinas} and \textit{O. Villamayor} [Prog. Math. 181, 147--227 (2000; Zbl 0969.14007)], and \textit{A. Bravo, S. Encinas} and \textit{O. Villamayor} [Rev. Mat. Iberoam. 21, No. 2, 349--458 (2005; Zbl 1086.14012)]) and their relationship with the weak equivalence introduced by Hironaka in the latest 70's, see for example [\textit{H. Hironaka}, ``Idealistic exponents of singularity'', Algebraic geometry, The Johns Hopkins centen. Lect., Symp. Baltimore/Maryland 1976, 52--125 (1977; Zbl 0496.14011)]. It simplifies some arguments and gives a very simple way to prove the ``naturality'' of the main step of the proof: the inductive step.
scientific article; zbMATH DE number 5833451
scientific article