Theorem 9 [03XQ]

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Theorem 9

(Weak factorization) Assume that $char\,k=0$ . Then for any two snc models ${\cal X},\,{\cal X}^{\prime}$ there exists a finite alternating sequence of simple blow-ups

{\cal X}<{\cal X}_{1}>{\cal X}_{2}<\dots<{\cal X}_{2m+1}>{\cal X}^{\prime}\,\,.