Counting lines on projective surfaces

2019/02/13 by Bauer, Thomas, Rams, Slawomir
#Algebraic Geometry (math.AG) #FOS: Mathematics #Primary: 14J25 #Secondary 14J70

paper · doi:10.48550/arxiv.1902.05133

Abstract

We prove a bound on the number of lines on a smooth degree-d surface in three-dimensional projective space for d ≥ 3. This bound improves a bound due to Segre and renders some of his arguments rigorous. It is the best known bound for d ≥ 6.

Related

• A bound for the number of lines lying on a nonsingular surface in 3-space over a finite field
• Counting lines on surfaces
• Smooth Surfaces with Maximal Lines
• Counting Surfaces Singular Along a Line in P³
• Numbers of points of surfaces in the projective 3-space over finite fields