Generic initial ideals of some monomial complete intersections in four variables

Abstract

Let R = K[x 1, x 2, x 3, x 4] be the polynomial ring over a field of characteristic zero. For the ideal $${(x_1^a, x_2^b, x_3^c, x_4^d) \subset R}$$ , where at least one of a, b, c and d is equal to two, we prove that its generic initial ideal with respect to the reverse lexicographic order is the almost revlex ideal corresponding to the same Hilbert function.