2025/08/06 by Granot, Eden
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2508.04426
We study points of moderately low degree on a curve C over a number field, which is embedded on a nice toric surface S. Recently, Smith and Vogt related the linear equivalence classes of such points to intersections of C with curves in the ambient surface. We show that when C is sufficiently effective and ample with simple singularities, all but finitely many sufficiently low degree points are obtained via intersections of C with curves in the ambient surface S. Our methods make use of the toric geometry of the ambient surface S to produce curves which interpolate the low degree points on C. Furthermore, we generalise a result by Debarre and Klassen to singular plane curves and higher degrees of points.