Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771553 | Finite Fields and Their Applications | 2017 | 16 Pages |
Abstract
Let F be a plane singular curve defined over a finite field Fq. 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 non-singular 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Nazar Arakelian,