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Toroidal varieties and the weak factorization theorem

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Abstract

We develop the theory of stratified toroidal varieties, which gives, together with the theory of birational cobordisms [73], a proof of the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field K of characteristic zero is a composite of blow-ups and blow-downs with smooth centers.

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  1. Department of Mathematics, Purdue University, IN 47907, West Lafayette, USA

    Jarosław Włodarczyk

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  1. Jarosław Włodarczyk
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Correspondence to Jarosław Włodarczyk.

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Dedicated to Professor Andrzej Białynicki-Birula

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Włodarczyk, J. Toroidal varieties and the weak factorization theorem. Invent. math. 154, 223–331 (2003). https://doi.org/10.1007/s00222-003-0305-8

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