A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension
代数几何
2007-05-23 v2
摘要
The recent two proofs for the (weak) factorization theorem for birational maps, one by W{\l}odarczyk and the other by Abramovich-Karu-Matsuki-W{\l}odarczyk rely on the results of Morelli. The former uses the process for -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.
引用
@article{arxiv.math/9803126,
title = {A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension},
author = {D. Abramovich and K. Matsuki and S. Rashid},
journal= {arXiv preprint arXiv:math/9803126},
year = {2007}
}
备注
the final and published version with minor mistakes corrected