Tangent cones of numerical semigroup rings

TL;DR

This paper characterizes the structure of tangent cones of numerical semigroup rings using classical invariants, providing explicit computational methods via GAP.

Contribution

It offers a detailed description of tangent cones of numerical semigroup rings and introduces computational techniques for their analysis.

Findings

Structure of tangent cones expressed through classical invariants.

Explicit computational methods implemented in GAP.

Enhanced understanding of the module structure over Noether normalization.

Abstract

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.