Propagating weights of tori along free resolutions

Federico Galetto

doi:10.1016/j.jsc.2015.05.004

Propagating weights of tori along free resolutions

Federico Galetto

Mathematics and Statistics

Queen’s University

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

4 Scopus citations

Abstract

The action of a torus on a graded module over a polynomial ring extends to the entire minimal free resolution of the module. We explain how to determine the action of the torus on the free modules in the resolution, when the resolution can be calculated explicitly. The problem is reduced to analyzing how the weights of a torus propagate along an equivariant map of free modules. The results obtained are used to design algorithms which have been implemented in the software system Macaulay2.

Original language	English
Pages (from-to)	1-45
Number of pages	45
Journal	Journal of Symbolic Computation
Volume	74
DOIs	https://doi.org/10.1016/j.jsc.2015.05.004
State	Published - May 1 2016

Keywords

Algorithm
Equivariant free resolution
Irreducible representation
Reductive group
Torus
Weight

Access to Document

10.1016/j.jsc.2015.05.004

Cite this

@article{dc313b7e672a4ebcbd031a15e090113f,

title = "Propagating weights of tori along free resolutions",

abstract = "The action of a torus on a graded module over a polynomial ring extends to the entire minimal free resolution of the module. We explain how to determine the action of the torus on the free modules in the resolution, when the resolution can be calculated explicitly. The problem is reduced to analyzing how the weights of a torus propagate along an equivariant map of free modules. The results obtained are used to design algorithms which have been implemented in the software system Macaulay2.",

keywords = "Algorithm, Equivariant free resolution, Irreducible representation, Reductive group, Torus, Weight",

author = "Federico Galetto",

year = "2016",

month = may,

day = "1",

doi = "10.1016/j.jsc.2015.05.004",

language = "English",

volume = "74",

pages = "1--45",

journal = "Journal of Symbolic Computation",

issn = "0747-7171",

publisher = "Academic Press",

}

TY - JOUR

T1 - Propagating weights of tori along free resolutions

AU - Galetto, Federico

PY - 2016/5/1

Y1 - 2016/5/1

N2 - The action of a torus on a graded module over a polynomial ring extends to the entire minimal free resolution of the module. We explain how to determine the action of the torus on the free modules in the resolution, when the resolution can be calculated explicitly. The problem is reduced to analyzing how the weights of a torus propagate along an equivariant map of free modules. The results obtained are used to design algorithms which have been implemented in the software system Macaulay2.

AB - The action of a torus on a graded module over a polynomial ring extends to the entire minimal free resolution of the module. We explain how to determine the action of the torus on the free modules in the resolution, when the resolution can be calculated explicitly. The problem is reduced to analyzing how the weights of a torus propagate along an equivariant map of free modules. The results obtained are used to design algorithms which have been implemented in the software system Macaulay2.

KW - Algorithm

KW - Equivariant free resolution

KW - Irreducible representation

KW - Reductive group

KW - Torus

KW - Weight

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84948720472&origin=inward

UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=84948720472&origin=inward

U2 - 10.1016/j.jsc.2015.05.004

DO - 10.1016/j.jsc.2015.05.004

M3 - Article

SN - 0747-7171

VL - 74

SP - 1

EP - 45

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

ER -

Propagating weights of tori along free resolutions

Abstract

Keywords

Access to Document

Other files and links

Cite this