Computing quotients by connected solvable groups

Gregor Kemper

doi:10.1016/j.jsc.2020.07.014

Computing quotients by connected solvable groups

Gregor Kemper

Chair of Algorithmic Algebra

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

Abstract

Consider an action of a connected solvable group G on an affine variety X. This paper presents an algorithm that constructs a semi-invariant f∈K[X]=:R and computes the invariant ring (R_f)^G together with a presentation. The morphism X_f→Spec((R_f)^G) obtained from the algorithm is a universal geometric quotient. In fact, it is even better than that: a so-called excellent quotient. If R is a polynomial ring, the algorithm requires no Gröbner basis computations. If R is a complete intersection, then so is (R_f)^G.

Original language	English
Pages (from-to)	426-440
Number of pages	15
Journal	Journal of Symbolic Computation
Volume	109
DOIs	https://doi.org/10.1016/j.jsc.2020.07.014
State	Published - 1 Mar 2022

Keywords

Algorithmic invariant theory
Geometric invariant theory
Geometric quotient
Solvable groups

Access to Document

10.1016/j.jsc.2020.07.014

Cite this

@article{9bd00402d298451cb44314d20a39dd9c,

title = "Computing quotients by connected solvable groups",

abstract = "Consider an action of a connected solvable group G on an affine variety X. This paper presents an algorithm that constructs a semi-invariant f∈K[X]=:R and computes the invariant ring (Rf)G together with a presentation. The morphism Xf→Spec((Rf)G) obtained from the algorithm is a universal geometric quotient. In fact, it is even better than that: a so-called excellent quotient. If R is a polynomial ring, the algorithm requires no Gr{\"o}bner basis computations. If R is a complete intersection, then so is (Rf)G.",

keywords = "Algorithmic invariant theory, Geometric invariant theory, Geometric quotient, Solvable groups",

author = "Gregor Kemper",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Ltd",

year = "2022",

month = mar,

day = "1",

doi = "10.1016/j.jsc.2020.07.014",

language = "English",

volume = "109",

pages = "426--440",

journal = "Journal of Symbolic Computation",

issn = "0747-7171",

publisher = "Academic Press",

}

TY - JOUR

T1 - Computing quotients by connected solvable groups

AU - Kemper, Gregor

PY - 2022/3/1

Y1 - 2022/3/1

N2 - Consider an action of a connected solvable group G on an affine variety X. This paper presents an algorithm that constructs a semi-invariant f∈K[X]=:R and computes the invariant ring (Rf)G together with a presentation. The morphism Xf→Spec((Rf)G) obtained from the algorithm is a universal geometric quotient. In fact, it is even better than that: a so-called excellent quotient. If R is a polynomial ring, the algorithm requires no Gröbner basis computations. If R is a complete intersection, then so is (Rf)G.

AB - Consider an action of a connected solvable group G on an affine variety X. This paper presents an algorithm that constructs a semi-invariant f∈K[X]=:R and computes the invariant ring (Rf)G together with a presentation. The morphism Xf→Spec((Rf)G) obtained from the algorithm is a universal geometric quotient. In fact, it is even better than that: a so-called excellent quotient. If R is a polynomial ring, the algorithm requires no Gröbner basis computations. If R is a complete intersection, then so is (Rf)G.

KW - Algorithmic invariant theory

KW - Geometric invariant theory

KW - Geometric quotient

KW - Solvable groups

UR - http://www.scopus.com/inward/record.url?scp=85087978093&partnerID=8YFLogxK

U2 - 10.1016/j.jsc.2020.07.014

DO - 10.1016/j.jsc.2020.07.014

M3 - Article

AN - SCOPUS:85087978093

SN - 0747-7171

VL - 109

SP - 426

EP - 440

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

ER -

Computing quotients by connected solvable groups

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this