A corollary to the Evans-Griffith Syzygy theorem
Let K be a field, S = K[x 1, … x n] be a polynomial ring in n variables over K and I ⊂ S be an ideal. We give a procedure to compute a prime filtration of S/I. We proceed as in the classical case by constructing an ascending chain of ideals of S starting from I and ending at S. The procedure of this paper is developed and has been implemented in the computer algebra system Singular.
We show that the natural generalization of a conjecture of Hain and Looijenga to the case of pointed curves holds for all and if and only if the tautological rings of the moduli spaces of curves with rational tails and of stable curves are Gorenstein.