Torification of diagonalizable group actions on toroidal schemes

Dan Abramovich; Michael Temkin

doi:https://doi.org/10.1016/j.jalgebra.2016.10.016

Torification of diagonalizable group actions on toroidal schemes

Dan Abramovich, Michael Temkin

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

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	American 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

Keywords

Diagonalizable groups
Group actions
Logarithmic structures
Toric geometry
Toroidal embeddings

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

https://doi.org/10.1016/j.jalgebra.2016.10.016

Cite this

@article{dcd9840dff704333be504c226192f74e,

title = "Torification of diagonalizable group actions on toroidal schemes",

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–W{\l}odarczyk, and Gabber in various aspects.",

keywords = "Diagonalizable groups, Group actions, Logarithmic structures, Toric geometry, Toroidal embeddings",

author = "Dan Abramovich and Michael Temkin",

note = "Funding Information: This research is supported by BSF grant 2010255 . Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

month = feb,

day = "15",

doi = "https://doi.org/10.1016/j.jalgebra.2016.10.016",

language = "American English",

volume = "472",

pages = "279--338",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Torification of diagonalizable group actions on toroidal schemes

AU - Abramovich, Dan

AU - Temkin, Michael

PY - 2017/2/15

Y1 - 2017/2/15

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84995624268&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.jalgebra.2016.10.016

DO - https://doi.org/10.1016/j.jalgebra.2016.10.016

M3 - Article

SN - 0021-8693

VL - 472

SP - 279

EP - 338

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Torification of diagonalizable group actions on toroidal schemes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this