On the Cohen–Macaulayness of tangent cones of monomial curves in $A^4(K)$

Abstract

In this paper we give necessary and sufficient conditions for the Cohen–Macaulayness of the tangent cone ofa monomial curve in 4-dimensional affine space. We particularly study the case where C is a Gorenstein noncompleteintersection monomial curve and we generalize some results in the literature. Moreover, by using these results, weconstruct families supporting Rossi’s conjecture, which is still open for monomial curves in 4-dimensional affine space.