Let $I_1,\dots <!--FUNCTION\; APPLICATION-->,I_n$ be ideals generated by linear forms in a polynomial ring over an infinite field and let $J=I_1\cdots I_n$. We describe a minimal free resolution of $J$ and show that it is supported on a polymatroid obtained from the underlying representable polymatroid by means of the so-called Dilworth truncation. Formulas for the projective dimension and Betti numbers are given in terms of the polymatroid as well as a characterization of the associated primes. Along the way we show that $J$ has linear quotients. In fact, we do this for a large class of ideals $J_P$, where $P$ is a certain poset ideal associated to the underlying subspace arrangement.

让${我}_1,\dots <!--FUNCTION\; APPLICATION-->,{我}_n$是在无限场上由多项式环中的线性形式生成的理想，并让$Ĵ={我}_1\cdots {我}_n$. 我们描述了一个最小的自由分辨率$Ĵ$并表明它支持通过所谓的 Dilworth 截断从底层可表示的 polymatroid 获得的 polymatroid。投影维数和 Betti 数的公式是根据 polymatroid 以及相关素数的表征给出的。一路走来，我们展示了$Ĵ$有线性商。事实上，我们这样做是为了一大类理想${Ĵ}_{磷}$， 在哪里$磷$是与底层子空间排列相关的某个定势理想。