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

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

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.

Erratum to: Birationally rigid hypersurfaces

This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new proof of the theorem.

论文《Weyl群与极小模型之间的双有理变换》的补遗/勘误

Addendum/Erratum to the paper "Weyl groups and Birational transformations among minimal models"

本文为1995年关于Fano三维簇与Weyl群论文的补遗和勘误，补入Mori–Mukai分类中遗漏的第88种形变类型，并修正相关错误与计算。