Gorenstein curves and symmetry of the semigroup of values
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- de la Mata, F.D. Manuscripta Math (1988) 61: 285. doi:10.1007/BF01258440
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LetO be the local ring of a irreducible algebroid curve and S its semigroup of values, Kunz in  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  (for the d=2 case) and the author in  (for arbitrary d) with the main goal of the explicit determination of S (in the case of plane curves).