Strengthening the Theorem of Embedded Desingularization

Resolution of singularities is one of the central areas of research in Algebraic Geometry. It is a basic prerequisite for the classification of algebraic varieties up to birational equivalence, since it allows to consider only regular varieties. Hironaka’s monumental work [Hi1] gave a non-constructive, existence proof of resolution of singularities over fields of characteristic zero. Constructive versions of Hironaka’s Theorem have been proposed in [BM], [V1], [V2] and [EV1], while simplified weak non-constructive versions can be found in [AJ], [AW] and [BP].