Abstract
Given an ideal I on a variety X with toroidal singularities, we produce a modification X0 → X, functorial for toroidal morphisms, making the ideal monomial on a toroidal stack X0. We do this by adapting the methods of [Wło05], discarding steps which become redundant. We deduce functorial resolution of singularities for varieties with logarithmic structures. This is the first step in our program to apply logarithmic desingularization to a morphism Z → B, aiming to prove functorial semistable reduction theorems.
Original language | English |
---|---|
Pages (from-to) | 3805-3866 |
Number of pages | 62 |
Journal | Journal of the European Mathematical Society |
Volume | 22 |
Issue number | 12 |
DOIs | |
State | Published - 4 Aug 2020 |
Bibliographical note
Publisher Copyright:© European Mathematical Society 2020. Keywords. Resolution of singularities, logarithmic geometry, algebraic stacks.