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

Let I be the Stanley–Reisner ideal of a simplicial complex Δ. In this short paper, we shall give a formula of vanishing of the local cohomology modules for S/I(r) in the case Δ 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).