Let $\mathcal A\subset\mathbb P^{k-1}$ be a rank $k$ arrangement of $n$hyperplanes, with the property that any $k$ of the defining linear forms arelinearly independent (i.e., $\mathcal A$ is called $k-$generic). We show thatfor any $j=0,\ldots,k-2$, the subspace arrangement with defining idealgenerated by the $(n-j)-$fold products of the defining linear forms of$\mathcal A$ is a set-theoretic complete intersection, which is equivalent tosaying that star configurations have this property.
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机译：假设$ \ mathcal A \ subset \ mathbb P ^ {k-1} $是$ n $超平面的等级$ k $排列，其性质是定义线性形式的任何$ k $都是线性独立的（即$ \数学A $称为$ k- $ generic）。我们表明对于任何$ j = 0，\ ldots，k-2 $，由定义的线性\ $ \ mathcal A $的$（nj）-$ fold乘积生成的具有定义理想的子空间排列是一个集合理论上的完备相交，相当于说星形配置具有此属性。
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