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A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension

D. Abramovich·K. Matsuki·S. Rashid
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Abstract

The recent two proofs for the (weak) factorization theorem for birational maps, one by Włodarczyk and the other by Abramovich-Karu-Matsuki-Włodarczyk rely on the results of Morelli. The former uses the process for $π$-desingularization (the most subtle part of Morelli's combinatorial algorithm), while the latter uses the strong factorization of toric (toroidal) birational maps directly. This paper provides a coherent account of Morelli's work (and its toroidal extension) clarifying some discrepancies in the original argument.

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D. Abramovich, K. Matsuki, S. Rashid. 2000-02-11. A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension. https://arxiv.org/abs/math/9803126

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