On the Cohen-Macaulayness of tangent cones of monomial curves in A(4)(K)

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