On the Gorenstein locus of some punctual Hilbert schemes

被引：27
|
作者：
Casnati, Gianfranco [1 ]
Notari, Roberto [2 ]
机构：
[1] Politecn Torino, Dipartimento Matemat, I-10129 Turin, Italy
[2] Politecn Milan, Dipartimento Matemat Francesco Brioschi, I-20133 Milan, Italy
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 2009年 / 213卷 / 11期
关键词：
STRUCTURE THEOREMS; ALGEBRAS; IDEALS; CODIMENSION; DIMENSION; FAMILIES; SPACE;
D O I：
10.1016/j.jpaa.2009.03.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let k be an algebraically closed field and let Hilb(d)(G)(P(k)(N)) be the open locus of the Hilbert scheme Hilb(d)(P(k)(N)) corresponding to Gorenstein subschemes. We prove that Hilb(d)(G)(P(k)(N)) is irreducible for d <= 9. Moreover we also give a complete picture of its singular locus in the same range d <= 9. Such a description of the singularities gives some evidence to a conjecture on the nature of the singular points in Hilb(d)(G)(P(k)(N)) that we state at the end of the paper. (C) 2009 Elsevier B.V. All rights reserved.
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页码：2055 / 2074
页数：20
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