Moduli of distributions via singular schemes

被引：3

作者：

Correa, Mauricio ^{[1
,2
]}

Jardim, Marcos ^{[3
]}

Muniz, Alan ^{[4
]}

机构：

[1] Univ Bari, Via E Orabona 4, I-70125 Bari, Italy

[2] Univ Fed Minas Gerais, Ave Antonio Carlos 6627, BR-30161970 Belo Horizonte, MG, Brazil

[3] Univ Estadual Campinas, Dept Matemat, IMECC, Rua Sergio Buarque de Holanda 651, BR-13083970 Campinas, SP, Brazil

[4] Univ Bourgogne & Franche Comte, Inst Math Bourgogne, UMR 5584, CNRS, 9 Ave Alain Savary,BP 47870, F-21078 Dijon, France

来源：

MATHEMATISCHE ZEITSCHRIFT | 2022年 / 301卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

Distributions; Hilbert scheme; Singular scheme; Syzygy; FOLIATIONS; SHEAVES; BUNDLES; SPACE;

D O I：

10.1007/s00209-022-03001-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a smooth projective variety. We show that the map that sends a codimension one distribution on X to its singular scheme is a morphism from the moduli space of distributions into a Hilbert scheme. We describe its fibers and, when X = P-n, compute them via syzygies. As an application, we describe the moduli spaces of degree 1 distributions on P-3. We also give the minimal graded free resolution for the ideal of the singular scheme of a generic distribution on P-3.

引用

页码：2709 / 2731

页数：23

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