Cohen_Macaulay modifications of squarefree monomial ideals

Abstract. Let be a field and be the polynomial ring in n variables over , and let be a squarefree Cohen_Macaulay monomial ideal in . Let be the set of monomial ideals with the property that the radical of coincides with . We are interested in the set of monomial ideals such that is Cohen_Macaulay. if and for all . Here the support of a monomial u is the . In Section 2 we show that the Stanley_Reisner ideal of the natural triangulation of the real projective plane has only trivial Cohen_Macaulay modifications.