2025/03/17 by Abramovich, Dan, Temkin, Michael, Włodarczyk, Jarosław
#14A20 #14A21 #14E15 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2503.13345
Theorem 1.2.6 of [ATW20] provides a relatively functorial logarithmic principalization of ideals on relative logarithmic orbifolds X→ B in characteristic 0, relying on a delicate monomialization theorem for Kummer ideals. The paper [AdSTW25] provides a parallel avenue through weighted blowings up. In this paper we show that, if X→ B is proper, monomialization of both Kummer and weighted logarithmic centers can be carried out in a manner which is functorial for base change by regular morphisms. This implies in particular logarithmic relative principalization of ideals and logarithmically smooth reduction of proper families of varieties in characteristic 0 in a manner equivariant for group actions and compatible with localization on the base.