Computing quotients by connected solvable groups. (March 2022)

• Record Type: Journal Article
• Authors: Kemper, Gregor
• Is Part Of: Journal of symbolic computation. Volume 109(2022)
• Page Start: 426
• Page End: 440
• Publication Date: 2022-03
• Subjects: 14L24 -- 13A50 -- 14L30; Algorithmic invariant theory -- Solvable groups -- Geometric invariant theory -- Geometric quotient; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.07.014
• Languages: English
• ISSNs: 0747-7171

Abstract

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 .