Resolution algorithms and deformations (Q2341556)

The author generalizes his paper [Rev. Mat. Iberoam. 25, No. 3, 995--1054 (2009; Zbl 1207.14009)] which gave an algorithmic resolution of singularities in characteristic zero. Here he develops a theory of simultaneous resolution completing his precedent results. The algorithm is an adaptation of the algorithm of \textit{S. Encinas} and \textit{O. Villamayor} [Prog. Math. 181, 147--227 (2000; Zbl 0969.14007)] and involves multi-ideals wich are essentially a pair consisting of a sheaf of ideals and a positive integer. This algorithm is classical if the object are defined over a field but has a real interest if they are defined over an artinian ring.