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Gröbner Bases of Symmetric Quotients and Applications

In: Algebra, Arithmetic and Geometry with Applications

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  • Ruth I. Michler

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!.

Suggested Citation

  • Ruth I. Michler, 2004. "Gröbner Bases of Symmetric Quotients and Applications," Springer Books, in: Chris Christensen & Avinash Sathaye & Ganesh Sundaram & Chandrajit Bajaj (ed.), Algebra, Arithmetic and Geometry with Applications, pages 627-637, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18487-1_37
    DOI: 10.1007/978-3-642-18487-1_37
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