Torification of diagonalizable group actions on toroidal schemes

Dan Abramovich; Michael Temkin

doi:10.1016/j.jalgebra.2016.10.016

Torification of diagonalizable group actions on toroidal schemes

Dan Abramovich^*, Michael Temkin

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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 language	English
Pages (from-to)	279-338
Number of pages	60
Journal	Journal of Algebra
Volume	472
DOIs	https://doi.org/10.1016/j.jalgebra.2016.10.016
State	Published - 15 Feb 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

Diagonalizable groups
Group actions
Logarithmic structures
Toric geometry
Toroidal embeddings

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10.1016/j.jalgebra.2016.10.016

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AB - 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.

KW - Diagonalizable groups

KW - Group actions

KW - Logarithmic structures

KW - Toric geometry

KW - Toroidal embeddings

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Torification of diagonalizable group actions on toroidal schemes

Abstract

Bibliographical note

Keywords

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