PROPERTIES OF T-SPREAD PRINCIPAL BOREL IDEALS GENERATED IN DEGREE TWO

摘要

In this paper, we have studied the stability of t-spread principal Borel ideals in degree two. We have proved that Ass(infinity)(I) = Min(I) U , where I = B-t (u) subset of S is a t-spread Borel ideal generated in degree 2 with u = x(i)x(n) t+1 <= i <= n - t. Indeed, I has the property that Ass(I-m) = Ass(I) for all m >= 1 and i <= t, in other words, I is normally torsion free. Moreover, we have shown that I is a set theoretic complete intersection if and only if u = x(n-t)x(n). Also, we have derived some results on the vanishing of Lyubeznik numbers of these ideals.