Simple Hironaka resolution in characteristic zero

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, no. 4 (2005): 779-822

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Building upon work of Villamayor and Bierstone-Milman we give a proof of the canonical Hironaka principalization and desingularization. The idea of "homogenized ideals" introduced in the paper gives {\it a priori} the canonicity of algorithm and radically simplifies the proof.

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