A Remark on the Local Cohomology Modules of a Union of Disjoint Matroids

Abstract

Let I be the Stanley-Reisner ideal of a simplicial complex . In this short paper, we shall give a formula of vanishing of the local cohomology modules for S/I (r) in the case is a union of disjoint matroids, where I (r) is the rth symbolic power of I . As an application, we will improve a previous result in Minh and Nakamura (Nagoya Math. J. 213, 127-140, 2014) for the k-Buchsbaumness of S/I (r) .