在1 × 1中三个胖点的整数上

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Korean Mathematical Society Pub Date : 2019-01-01 DOI:10.4134/JKMS.j180385

G. Favacchio, E. Guardo

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引用次数: 2

摘要

在这些笔记中，我们引入了一个数值函数，它允许我们显式地(非递归地)描述Betti数，因此，三个胖点的集合Z的希尔伯特函数，其支持是P1 × P1中的几乎完全相交(ACI)。即使对于P2中特殊支撑点上的5个点的对应集合，也很难给出这些构型的Betti数和Hilbert函数的非递归公式，我们在文献中也没有发现任何这样的结果。此外，我们还给出了一个判据，使我们能够描述这些特殊胖点集的希尔伯特函数。

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ON THE BETTI NUMBERS OF THREE FAT POINTS IN ℙ 1 × ℙ 1

In these notes we introduce a numerical function which allows us to describe explicitly (and nonrecursively) the Betti numbers, and hence, the Hilbert function of a set Z of three fat points whose support is an almost complete intersection (ACI) in P1 × P1. A nonrecursively formula for the Betti numbers and the Hilbert function of these configurations is hard to give even for the corresponding set of five points on a special support in P2 and we did not find any kind of this result in the literature. Moreover, we also give a criterion that allows us to characterize the Hilbert functions of these special set of fat points.

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来源期刊

Journal of the Korean Mathematical Society 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).