JournalsjemsVol. 22, No. 12pp. 3805–3866

Principalization of ideals on toroidal orbifolds

  • Dan Abramovich

    Brown University, Providence, USA
  • Michael Temkin

    The Hebrew University of Jerusalem, Israel
  • Jarosław Włodarczyk

    Purdue University, West Lafayette, USA
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Abstract

Given an ideal I\mathcal I on a variety XX with toroidal singularities, we produce a modification XXX' \to X, functorial for toroidal morphisms, making the ideal monomial on a toroidal stack XX'. 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 ZBZ \to B, aiming to prove functorial semistable reduction theorems.

Cite this article

Dan Abramovich, Michael Temkin, Jarosław Włodarczyk, Principalization of ideals on toroidal orbifolds. J. Eur. Math. Soc. 22 (2020), no. 12, pp. 3805–3866

DOI 10.4171/JEMS/997