NON-COHEN-MACAULAY SYMBOLIC BLOW-UPS FOR SPACE MONOMIAL CURVES AND COUNTEREXAMPLES TO COWSIK QUESTION

Let A = k[[X, Y, Z]] and k[[T]] be formal power series rings over a field k , and let n > 4 be an integer such that n not-equal 0 mod 3. Let phi:A - k[[T]] denote the homomorphism of k-algebras defined by phi(X) = T7n-3, phi(Y) = T(5n-2)n, and phi(Z) = T8n-3. We put p = Kerphi. Then R(s)(p) = +igreater-than-or-equal-to0p(i) is a Noetherian ring if and only if chk > 0. Hence on Cowsik's question there are counterexamples among the prime ideals defining space monomial curves, too.