On Pseudo Symmetric Monomial Curves

TL;DR

This paper investigates the algebraic and geometric properties of monomial curves associated with 4-generated pseudo symmetric numerical semigroups, focusing on binomials, resolutions, and Cohen-Macaulay tangent cones.

Contribution

It provides a characterization of indispensable binomials, conditions for strongly indispensable resolutions, and Cohen-Macaulay tangent cones for these monomial curves.

Findings

Identified indispensable binomials of the toric ideals.

Characterized when the monomial algebras have strongly indispensable resolutions.

Determined conditions for tangent cones to be Cohen-Macaulay.

Abstract

In this article, we study monomial curves, toric ideals and monomial algebras associated to $4$-generated pseudo symmetric numerical semigroups. Namely, we determine indispensable binomials of these toric ideals, give a characterization for these monomial algebras to have strongly indispensable minimal graded free resolutions. We also characterize when the tangent cones of these monomial curves at the origin are Cohen-Macaulay.