On monomial curves obtained by gluing

TL;DR

This paper investigates the algebraic properties of tangent cones of affine monomial curves constructed via gluing, providing characterizations of Cohen-Macaulay and Gorenstein properties and introducing new families with non-decreasing Hilbert functions.

Contribution

It offers new characterizations of tangent cone properties for monomial curves obtained by gluing and introduces novel families with specific Hilbert function behaviors.

Findings

Characterization of Cohen-Macaulay tangent cones

Identification of Gorenstein tangent cones

Construction of new monomial curve families with non-decreasing Hilbert functions

Abstract

We study arithmetic properties of tangent cones associated to affine monomial curves, using the concept of gluing. In particular we characterize the Cohen-Macaulay and Gorenstein properties of tangent cones of some families of monomial curves obtained by gluing. Moreover, we provide new families of monomial curves with non--decreasing Hilbert functions.