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math.AG2004
Simple Hironaka resolution in characteristic zero
Jaroslaw Wlodarczyk
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…
math.AG1999
Birational cobordisms and factorization of birational maps
Jaroslaw Wlodarczyk
In this paper we develop a Morse-like theory in order to decompose birational maps and morphisms of smooth projective varieties defined over a field of characteristic zero into mor…
math.AG1999
Torification and Factorization of Birational Maps
Dan Abramovich, Kalle Karu, Kenji Matsuki +1
Building on the work of the fourth author in math.AG/9904074, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between comple…