On the reduction numbers and the Castelnuovo-Mumford regularity of projective monomial curves

TL;DR

This paper provides explicit formulas for key algebraic invariants, the reduction number and Castelnuovo-Mumford regularity, of projective monomial curves, aiding in their algebraic and geometric analysis.

Contribution

It introduces explicit formulas for the reduction number and Castelnuovo-Mumford regularity of projective monomial curves, advancing understanding of their algebraic properties.

Findings

Derived explicit formulas for reduction number

Computed Castelnuovo-Mumford regularity explicitly

Enhanced algebraic understanding of projective monomial curves

Abstract

This paper gives explicit formulas for the reduction number and the Castelnuovo-Mumford regularity of projective monomial curves.