2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59356This is an erratum to math.AG/9803126, Tohoku 51 (1999) 489-537. This erratum describes: 1. the failure of the algorithm in [AMR] and [Morelli1] for the strong factorization pointed out by Kalle Karu, 2. the statement of a refined weak factorization theorem for toroidal birational morphisms in [AMR], in the form utilized in [AKMR] for the proof of the weak factorization theorem for general birationla maps, avoiding the use of the above mentioned algorithm for the strong factorization, and 3. a list of corrections for a few other mistakes in [AMR], mostly pointed out by Laurent Bonavero.3 pagesAlgebraic Geometry14E05;14M25Erratum to the paper "A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension"text