Hilbert function and resolution of the powers of the ideal of the rational normal curve (Q1582732)

The author studies the ideals mentioned in the title. If \(P\) denotes the ideal defining the rational normal curve, he computes the regularity of the power \(P^h\) and the symbolic power \(P^{(h)}\). Then he proceeds to find the Hilbert function, the Hilbert polynomial, and the Betti numbers of \(P^h\). In the case of \(P^{(h)}\), his calculation works only for \(h\leq 3\) or for \(n\leq 4\). Finally the Hilbert function of the module of Kähler differentials of \(K[x_0,\dots, x_n]/P\) is derived from \(P^{(2)}\).