Principalization of ideals on toroidal orbifolds

Dan Abramovich, Michael Temkin, Jarosław Włodarczyk

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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 languageAmerican English
Pages (from-to)3805-3866
Number of pages62
JournalJournal of the European Mathematical Society
Volume22
Issue number12
DOIs
StatePublished - 4 Aug 2020

Bibliographical note

Publisher Copyright:
© European Mathematical Society 2020. Keywords. Resolution of singularities, logarithmic geometry, algebraic stacks.

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