Abstract . In this paper we consider numerical semigroups S generated by arithmetic sequences m_0, m_n ( AS semigroups ) . First we state some results on the module T1 of k[S] ; further in the cases m_0≡ 1 and m_0≡ n ( modulo n ) , we prove these semigroups are Weierstrass by showing that the associated monomial curves X = Spec K[S] are smoothable. Finally for each semigroup S generated by an arithmetic sequence we evaluate the so–called “order bounds” : when S is Weierstrass, these invariants are good approximations for the minimum distance of the related one–point codes .
Smoothability and order bound for AS semigroups
ONETO, ANNA;TAMONE, GRAZIA
2012-01-01
Abstract
Abstract . In this paper we consider numerical semigroups S generated by arithmetic sequences m_0, m_n ( AS semigroups ) . First we state some results on the module T1 of k[S] ; further in the cases m_0≡ 1 and m_0≡ n ( modulo n ) , we prove these semigroups are Weierstrass by showing that the associated monomial curves X = Spec K[S] are smoothable. Finally for each semigroup S generated by an arithmetic sequence we evaluate the so–called “order bounds” : when S is Weierstrass, these invariants are good approximations for the minimum distance of the related one–point codes .
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