The flecnode polynomial: a central object in incidence geometry

2014/04/13 by Katz, Nets Hawk
#Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.3412

Abstract

We give a brief exposition of the proof of the Cayley-Salmon theorem and its recent role in incidence geometry. Even when we don't use the properties of ruled surfaces explicitly, the regime in which we have interesting results in point-line incidence problems often coincides with the regime in which lines are organized into ruled surfaces.

Related

• Ruled surface theory and incidence geometry
• On some points-and-lines problems and configurations
• Incidences and tilings
• Absolute incidence theorems and tilings
• New quantitative estimates on the incidence geometry and growth of finite sets