Unmixedness and arithmetic properties of matroidal ideals

Abstract

Let $R=k[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $k$ and $I$ be a matroidal ideal of degree $d$. In this paper, we study the unmixedness properties and the arithmetical rank of $I$. Moreover, we show that $ara(I)=n-d+1$. This answer to the conjecture that made by H. J. Chiang-Hsieh \cite[Conjecture]{C}.