NON-COHEN-MACAULAY SYMBOLIC BLOW-UPS FOR SPACE MONOMIAL CURVES

Let p = p(n1, n2, n3) denote the prime ideal in the formal power series ring A = k[[X, Y, Z]] over a field k defining the space monomial curve X = T(n)1 , Y = T(n)2 , and Z = T(n)3 with GCD(n1 , n2, n3) = 1 . Then the symbolic Rees algebra R(s)(p) = +n greater-than-or-equal-to 0 p(n) for p = p(n2 + 2n + 2, n2 + 2n + 1 , n2 + n + 1) is Noetherian but not Cohen-Macaulay if ch k = p > 0 and n = p(e) with e greater-than-or-equal-to 1 . The same is true for p = p(n2, n2 + 1, n2 + n + 1) if ch k = p > 0 and n = p(e) greater-than-or-equal-to 3.