manuscripta mathematica

, Volume 61, Issue 3, pp 285–296

Gorenstein curves and symmetry of the semigroup of values


  • Félix Delgado de la Mata
    • Dto. Algebra y GeometríaUniversidad de Valladolid

DOI: 10.1007/BF01258440

Cite this article as:
de la Mata, F.D. Manuscripta Math (1988) 61: 285. doi:10.1007/BF01258440


LetO be the local ring of a irreducible algebroid curve and S its semigroup of values, Kunz in [7] proves thatO is a Gorenstein ring if and only if S is symmetrical. In this paper we give a generalization of this fact for the case of reduced curves with an arbitrary number of branches, d. For it we introduce a concept of symmetry for the semigroup of values S⊂ℤ+ d which generalizes the well known symmetry for d=1 (i.e. the irreducible case). This concept of symmetry is also closely related to the symmetry introduced by García in [4] (for the d=2 case) and the author in [3] (for arbitrary d) with the main goal of the explicit determination of S (in the case of plane curves).

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© Springer-Verlag 1988