A Minimal Free Resolution for Certain Monomial Curves in 𝔸⁴

Abstract

Abstract Let K be a field and m 0 <ċ< m 3 be coprime positive integers, which form an arithmetic progression. Let 𝒞 be a monomial curve in the affine 4-space , defined parametrically by X 0 = T m 0 ,…, X 3 = T m 3 . Let A be the coordinate ring of 𝒞. In this article, we produce an explicit minimal free resolution for A.