Numerical semigroups and applications
Abdallah Assi (LAREMA), Pedro A. Garc\'ia-S\'anchez
TL;DR
This paper introduces fundamental concepts of numerical semigroups, illustrating their applications in analyzing singularities of algebraic curves and providing examples of nonunique factorization invariants.
Contribution
It offers a comprehensive overview of numerical semigroups and demonstrates their utility in algebraic geometry and factorization theory.
Findings
Numerical semigroups help analyze singularities of plane algebraic curves.
They provide examples of nonunique factorization invariants.
The paper clarifies basic notions and applications of numerical semigroups.
Abstract
The aim of this manuscript is to give some basic notions related to numerical semigroups, and from these on the one hand describe a classical application to the study of singularities of plane algebraic curves, and on the other, show how numerical semigroups can be used to obtain handy examples of nonunique factorization invariants.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Advanced Numerical Analysis Techniques