Buchsbaumness of ordinary powers of two-dimensional square-free monomial ideals

摘要

Let S=k[x_1,x_2,..,x_n] be a polynomial ring. Let I be a Stanley-Reisner ideal in S of a pure simplicial complex of dimension one. In this paper, we study the Buchsbaum property of S/Ir for any integer r>0. Our first purpose is giving a characterization of Ext-modules ExtSp(S/mt,S/J) for any monomial ideal J, where mt=(x_(_1~t),x_(_2~t),..,x_(~n_t)), in terms of certain simplicial complexes. Then we consider the Buchsbaum property of S/I~r. The main tool to check the Buchsbaumness is the surjectivity criterion. We see the behavior of the canonical map from ExtSp(S/mt,S/I~r) to H_m~p(S/I~r) from the view point of reduced cohomology groups of simplicial complexes.