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

作者：Arakelian Nazar^*

来源：Finite Fields and Their Applications, 2017, 48: 87-102.

DOI：10.1016/j.ffa.2017.07.004

• Algebraic curves
• Rational points
• Finite fields

Let F be a plane singular curve defined over a finite field F-q. Via results of [11] and [1], the linear system of plane curves of a given degree passing through the singularities of F provides potentially good bounds for the number of points on a nonsingular model of F. In this note, the case of a curve with two singularities such that the sum of their multiplicities is precisely the degree of the curve is investigated in more depth. In particular, such plane models are completely characterized, and for p > 3, a curve of this type attaining one of the obtained bounds is presented.

• 出版日期2017-11