Deforming monomial space curves into set-theoretic complete intersection singularities

TL;DR

This paper explores deforming monomial space curves to create examples of set-theoretic complete intersection singularities, also providing an inverse to Herzog's construction related to numerical semigroups.

Contribution

It introduces a method to deform monomial space curves into set-theoretic complete intersections and describes an inverse process to Herzog's construction for certain numerical semigroups.

Findings

Constructed examples of set-theoretic complete intersection singularities

Described an inverse to Herzog's minimal generators construction

Provided new insights into the structure of numerical semigroups

Abstract

We deform monomial space curves in order to construct examples of set-theoretical complete intersection space curve singularities. As a by-product we describe an inverse to Herzog's construction of minimal generators of non-complete intersection numerical semigroups with three generators.