On the Hilbert Function of General Fat Points in P1 x P1

被引：0

作者：

Carlini, Enrico ^{[1
]}

Catalisano, Maria Virginia ^{[2
]}

Oneto, Alessandro ^{[3
]}

机构：

[1] Politecn Torino, DISMA Dept Math Sci, Turin, Italy

[2] Univ Genoa, Dipartimento Ingn Meccan Energet Gest & Trasporti, Genoa, Italy

[3] Otto von Guericke Univ, Fak Math IAG, Magdeburg, Germany

来源：

MICHIGAN MATHEMATICAL JOURNAL | 2020年 / 69卷 / 03期

关键词：

LINEAR-SYSTEMS; BASE POINTS; CURVES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the bi-graded Hilbert function of ideals of general fat points with same multiplicity in P-1 x P-1. Our first tool is the multiprojective-affine-projective method introduced by the second author in previous works with A. V. Geramita and A. Gimigliano where they solved the case of double points. In this way, we compute the Hilbert function when the smallest entry of the bi-degree is at most the multiplicity of the points. Our second tool is the differential Horace method introduced by J. Alexander and A. Hirschowitz to study the Hilbert function of sets of fat points in standard projective spaces. In this way, we compute the entire bi-graded Hilbert function in the case of triple points.

引用

页码：601 / 632

页数：32

共 21 条

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