Punctual hilbert schemes of small length in dimensions 2 and 3
Punctual hilbert schemes of small length in dimensions 2 and 3
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2 维和 3 维小长度正时希尔伯特方案
DOI：
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发表时间：
2000
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通讯作者：
S. Tikhomirov
中科院分区：
文献类型：
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作者：
S. Tikhomirov
2维和3维的点希尔伯特格式的双正则几何，即，研究了光滑曲面或光滑三维簇上给定点支撑的定长零维子格式的参数化格式。一个精确的双正则描述这些计划已被称为只有平凡的情况下，长度为3和4的2维。下一个情况下的长度5在2维和两个第一个非平凡的情况下的长度3和4在3维考虑。本文详细地描述了点希尔伯特格式的双正则性质及其通过各种完全点标志的自然指定。
The biregular geometry of punctual Hilbert schemes in dimensions 2 and 3, i.e., of schemes parametrizing fixed-length zero-dimensional subschemes supported at a given point on a smooth surface or a smooth three-dimensional variety, is studied. A precise biregular description of these schemes has only been known for the trivial cases of lengths 3 and 4 in dimension 2. The next case of length 5 in dimension 2 and the two first nontrivial cases of lengths 3 and 4 in dimension 3 are considered. A detailed description of the biregular properties of punctual Hilbert schemes and of their natural designularizations by varieties of complete punctual flags is given.