On the Hilbert Series of the tangent cones for some 4-generated pseudo 2 symmetric monomial curves

TL;DR

This paper investigates the Hilbert Series of tangent cones for specific 4-generated pseudo symmetric monomial curves, providing explicit computations of the Hilbert function and standard bases of associated toric ideals.

Contribution

It offers new explicit calculations of Hilbert functions and standard bases for tangent cones of certain monomial curves, especially in non-Cohen-Macaulay cases.

Findings

Hilbert function is nondecreasing for studied tangent cones

Explicit standard bases of toric ideals are computed

Provides detailed Hilbert Series analysis for specific monomial curves

Abstract

In this article, we study Hilbert Series of non-Cohen-Maculay tangent cones for some 4-generated pseudo symmetric monomial curves. We show that the Hilbert Function is nondecreasing by explicitly computing it. We also compute standard bases of these toric ideals.