Smoothability and order bound for AS semigroups

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 $T^{1}_{kS]}$ ; 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 $X=\operatorname {Spec}{kS]}$ 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.