POINTED SIMPLICIAL COMPLEXES

摘要

For what follows, R is k[x_1,..., x_n], k is a field of characteristic p, I is a monomial ideal of R and M = R/I. The ranks of the free modules that appear in a minimal free resolution of M might depend on p. It is well known that the zeroth and nth betti number of M are independent of p. Bruns and Herzog, [BrHe95] show that if n ≤ 5 all betti numbers of M are independent of p. In the same paper they show that for i = 1, 2, n - 1, the i th betti number of M is always independent of p. Terai and Hibi [TeHia] show that the third and fourth betti numbers are independent of p when I is generated by monomials of degree 2 and also prove that the betti numbers are independent of k in some other cases as well [TeHia], [TeHib]. The most familiar classes of monomial ideals whose betti numbers are independent of p include (a) monomial ideals which are generated by R-sequences, (b) stable monomial ideals [ElKe90], and (c) squarefree stable ideals [ArHeHi95], [ChEv93].