Work

Deriving Newton's Canonical Forms of Cubic Curves via the Center of Polynomials

Year: 2026

Type: preprint

Abstract: Existing classifications of real plane cubic curves rely on sophisticated tools and require a lengthy exposition. This paper provides a concise yet elementary treatment of this classical topic. Using the centers of polynomials, we establish a correspondence between the algebraic structure of these centers and geometric properties of binary cubic polynomials, which yields a novel approach to Newton's canonical forms.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.09601

Authors: Huang, Hua-Lin, Liao, Lili, Ye, Yu, Yuan, Ziqi

Institutions: Huaqiao University, Anhui University, University of Science and Technology of China

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Fujian Province, National Science and Technology Major Project

Awards: G1342967929, G2387255867, G3685485237, G3857364911, G4656525603, G5592559879

OpenAlex ID: W7212139132

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