Torification of diagonalizable group actions on toroidal schemes
arXiv:1407.2629
Abstract
We study actions of diagonalizable groups on toroidal schemes (i.e. logarithmically regular logarithmic schemes). In particular, we show that for so-called toroidal actions the quotient is again a toroidal scheme. Our main result constructs for an arbitrary action a canonical torification - making the action toridal after an equivariant blowings up. This extends earlier results of Abramovich-de Jong, Abramovich-Karu-Matsuki-Włodarczyk, and Gabber in various aspects.
The statement of the main result was again strengthened to accommodate our work on functorial factorization of birational maps: we now blow up an ideal without need to further normalize, using results in the new section 5. Some errors were corrected, in particular we made the functorial choice of a torific ideal more precise