D. Abramovich et al., A note on the factorization theorem of toric birational maps after Morelliand its toroidal extension, TOHOKU MATH, 51(4), 1999, pp. 489-537
Building upon a work of Morelli, we give a coherent presentation of Morelli
's algorithm for the weak and strong factorization of toric birational maps
. We also discuss its toroidal extension, which plays a crucial role in the
recent solutions by Wlodarczyk and Abramovich-Karu-Matsuki-Wlodarczyk of t
he weak factorization conjecture of general birational maps.