Tangent cones of numerical semigroup rings

In this paper we describe the structure of the tangent cone of a numerical semigroup ring \(A=k[[S]] \subseteq k[[t]]\) with multiplicity \(e\) (as a module over the Noether normalization determined by the fiber cone of the ideal generated by \(t^e\)) in terms of some classical invariants of the corresponding numerical semigroup. Explicit computations are also made by using the GAP system.