Monomial curve families supporting Rossiʼs conjecture

In this article, we give a constructive method to form infinitely many families of monomial curves in affine 4-space with corresponding Gorenstein local rings in embedding dimension 4 supporting Rossiʼs conjecture. Starting with any monomial curve in affine 2-space, we obtain large families of Gorenstein local rings with embedding dimension 4, having non-decreasing Hilbert functions, although their associated graded rings are not Cohen–Macaulay.