CELLULAR DECOMPOSITIONS FOR NESTED HILBERT SCHEMES OF POINTS
CELLULAR DECOMPOSITIONS FOR NESTED HILBERT SCHEMES OF POINTS
复制标题
嵌套希尔伯特点方案的细胞分解
DOI：
10.2140/pjm.1998.183.39
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发表时间：
1998
影响因子：
0.6
通讯作者：
Jan Cheah
中科院分区：
文献类型：
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作者：
Jan Cheah
其中符号 n 用作 m 元组 (n1, n2, .., nm) 的简写。该简写将在整篇论文中使用。当然，当我们研究这样的空间时，假设 n1 < n2 < ... < nm 并不失一般性。空间 Zn(X) 的构造作为方案是对 [Gr]、[Kol] 和 [Mum] 中的 HilbX 构造的简单修改（详细信息请参见 [Ch1]）。我们还考虑简化方案，参数化集中在某个固定点 P 的平滑簇 X 的长度为 n (n ≥ 1) 的零维子方案。如果 X 的维度为 r，则该方案可以用参数化 A 集中在原点的长度为 n 的零维子方案的简化方案来识别，因此用 Hilb(A, 0) 表示。或者，Hilb(A, 0) 与 Hilb(Spec (C[[x1, x2, ..., xr]])) 的简化方案一致，希尔伯特方案参数化 Spec (C [[x1, x2, ..., xr]]) 的长度为 n 的子方案。和以前一样，我们可以考虑以下形式的嵌套希尔伯特方案
where the symbol n is used as a shorthand for the m-tuple (n1, n2, .., nm). This shorthand will be used throughout the paper. There is, of course, no loss of generality in assuming that n1 < n2 < ... < nm when we study such a space. The construction of the spaces Zn(X) as schemes is a simple modification of the construction of HilbX found in [Gr], [Kol] and [Mum] (see [Ch1] for details). We also consider the reduced scheme parametrizing zero-dimensional subschemes of length n (n ≥ 1) of a smooth variety X concentrated at some fixed point P . If X has dimension r, this scheme can be identified with the reduced scheme parametrizing zero-dimensional subschemes of length n of A concentrated at the origin and is hence denoted by Hilb(A, 0). Alternatively, Hilb(A, 0) agrees with the reduced scheme of Hilb(Spec (C[[x1, x2, . . . , xr]])), the Hilbert scheme parametrizing subschemes of length n of Spec (C [[x1, x2, ..., xr]]). As before, one can consider nested Hilbert schemes of the form