On the geometric structure of finite sets of points in P^2

Pham Truc Lam * and Tran Thi Anh Phuong

* Corresponding author: (ptlam@dhsphue.edu.vn)

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Received: Jul 20, 2026
Revised: Sep 16, 2026
Accepted: Sep 17, 2026
Published:
Title: On the geometric structure of finite sets of points in P^2
Section
Journal of Science and Education: Natural Science - Technology

Abstract

Given a finite set X of s distinct points in the projective space P^n, we are interested in studying its uniformity property. When n=2 and X is (i,j)-uniform, we establish a sufficient condition for X to lie on a curve of degree at most 2.
Keywords: Sets of points, Cayley–Bacharach property, Plane configurations, Uniformity property

Tóm tắt

Với X là một tập hữu hạn gồm s điểm phân biệt trong không gian xạ ảnh P^n, chúng tôi quan tâm đến việc nghiên cứu tính đều của tập điểm đó. Khi n=2 và X là (i,j)-đều, chúng tôi thiết lập một điều kiện đủ để X nằm trên một đường cong có bậc không vượt quá 2.
Từ khóa: Các tập điểm, Tính Cayley–Bacharach, Các cấu hình phẳng, Tính đều

Article Details

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