Gorenstein curves and symmetry of the semigroup of values |
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Authors: | Félix Delgado de la Mata |
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Institution: | (1) Dto. Algebra y Geometría, Universidad de Valladolid, Pdo. de la Magdalena s/n, 47005 Valladolid, Spain |
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Abstract: | 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+
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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