Bierstone, Edward; Milman, Pierre D. Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant. (English) Zbl 0896.14006 Invent. Math. 128, No. 2, 207-302 (1997). In this paper the authors give an elementary and constructive proof of Hironaka’s celebrated theorem on resolutions of singularities in characteristic zero. They introduce a discrete local invariant whose maximum locus determines a smooth centre for blowing up. This then leads to desingularization. There are many examples in the paper. Reviewer: T.de Jong (Saarbrücken) Cited in 21 ReviewsCited in 227 Documents MSC: 14E15 Global theory and resolution of singularities (algebro-geometric aspects) Keywords:resolutions of singularities; discrete local invariant PDFBibTeX XMLCite \textit{E. Bierstone} and \textit{P. D. Milman}, Invent. Math. 128, No. 2, 207--302 (1997; Zbl 0896.14006) Full Text: DOI arXiv