论文标题
在投影空间中确定要点理想的限制
Identifying limits of ideals of points in the case of projective space
论文作者
论文摘要
我们研究了与标准分级多项式环的多层希尔伯特方案中的根部理想源的封闭，以及在投影空间中一般位置位置的均质坐标环的希尔伯特函数。在投影平面的情况下，我们给出了足够的条件，使理想成为激进理想基因座的封闭。对于任意维度的投射空间，我们提出了必要的条件。该论文是由边界极性引理的动机，将这种多层希尔伯特方案与多项式等级理论联系起来。
We study the closure of the locus of radical ideals in the multigraded Hilbert scheme associated with a standard graded polynomial ring and the Hilbert function of a homogeneous coordinate ring of points in general position in projective space. In the case of projective plane, we give a sufficient condition for an ideal to be in the closure of the locus of radical ideals. For projective space of arbitrary dimension we present a necessary condition. The paper is motivated by the border apolarity lemma which connects such multigraded Hilbert schemes with the theory of ranks of polynomials.
