Gröbner Bases of Symmetric Quotients and Applications

Ruth I. Michler

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 627-637 from Springer

Abstract: Abstract In this paper, we define the universal Σ-Gröbner basis. This Gröbner basis allows for an enumeration of elements in Σ-orbits and hence computes a Gröbner basis for symmetric quotients of the polynomial ring K[X 1,…, X n] on which the symmetric group Σ of degree N operates by permuting the variables. In certain cases the universal Σ -Gröbner basis coincides with the usual Gröbner basis with the total degree reverse lexicographic ordering. We will illustrate such a case by explicit computations of Gröbner bases for the ideals defining the singular locus of a class of hypersurfaces A in A K N with only isolated singularities. The number of generators of the torsion modules of differentials Torsion (Ω A/K N-1 ) of these hypersurfaces is N!.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_37

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DOI: 10.1007/978-3-642-18487-1_37

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