Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals

Let I be a monomial ideal in a polynomial ring R = k [ x 1 , … , x r ] . In this paper, we give an upper bound on dstab ¯ ( I ) in terms of r and the maximal generating degree d ( I ) of I such that depth R / I n ¯ is constant for all n ⩾ dstab ¯ ( I ) . As an application, we classify the class of monomial ideals I such that I n ¯ is Cohen-Macaulay for some integer n ≫ 0.