Number of rational branches of a plane singular curve over a finite\n field

2016/12/20 by Nazar Arakelian, Arakelian, Nazar · 1 citation
Computer Science · Mathematics · Social Sciences · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Communism, Protests, Social Movements #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1612.06652

openalex publication_date 2016/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \F be a plane singular curve defined over a finite field\n mathbbF_q. The linear system of plane curves of a given degree passing\nthrough the singularities of cF provides potentially good bounds for the\nnumber of points on a non-singular model of \F. In this note, the\ncase of a curve with two singularities such that the sum of their\nmultiplicities is precisely the degree of the curve is investigated in more\ndepth. In particular, such plane models are completely characterized, and for\np > 3, a curve of this type attaining one of the obtained bounds is\npresented.\n

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