In this paper, we investigate the behavior of almost reverse lexicographic ideals with the Hilbert function of a complete intersection. More precisely, over a field K, we give a new constructive proof of the existence of the almost revlex ideal \(J\subset K[x_1,\ldots ,x_n]\), with the same Hilbert function as a complete intersection defined by n forms of degrees \(d_1\le \cdots \le d_n\). Properties of the reduction numbers for an almost revlex ideal have an important role in our inductive and constructive proof, which is different from the more general construction given by Pardue in 2010. We also detect several cases in which an almost revlex ideal having the same Hilbert function as a complete intersection corresponds to a singular point in a Hilbert scheme. This second result is the outcome of a more general study of lower bounds for the dimension of the tangent space to a Hilbert scheme at stable ideals, in terms of the number of minimal generators.

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关于具有完整交点的希尔伯特函数的几乎可逆的理想

在本文中，我们用一个完整的交点的希尔伯特函数研究了几乎反向的词典理想的行为。更确切地说，在字段K上，我们给出了一个近似构造理想\（J \ subset K [x_1，\ ldots，x_n] \）的存在的新构造性证明，其中希尔伯特函数与由n个度数形式\（d_1 \ le \ cdots \ le d_n \）。近似可复性理想的归约数的性质在归纳和构造证明中起着重要作用，这与Pardue在2010年给出的更一般的构造不同。我们还检测到几种情况，其中近似可复性理想具有相同的希尔伯特作为完整交集的函数对应于希尔伯特方案中的奇异点。第二个结果是根据最小生成器的数量，对稳定理想状态下的希尔伯特方案的切空间的维数下界进行更一般性研究的结果。