Torification of diagonalizable group actions on toroidal schemes

Dan Abramovich*, Michael Temkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 by an equivariant blowings up. This extends earlier results of Abramovich–de Jong, Abramovich–Karu–Matsuki–Włodarczyk, and Gabber in various aspects.

Original languageAmerican English
Pages (from-to)279-338
Number of pages60
JournalJournal of Algebra
StatePublished - 15 Feb 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.


  • Diagonalizable groups
  • Group actions
  • Logarithmic structures
  • Toric geometry
  • Toroidal embeddings


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