Rational quintics in the real plane

Abstract

From a topological viewpoint, a rational curve in the real projective plane is generically a smoothly immersed circle and a finite collection of isolated points. We give an isotopy classification of generic rational quintics in ${\mathbb{RP}}^2$ in the spirit of Hilbert's 16th problem.

73 pages, update to accepted version (Transactions of the AMS)

References in corpus (3)

• Enumerative tropical algebraic geometry in R2
• Brief introduction to tropical geometry
• Rigid isotopy classification of real degree-4 planar rational curves with only real nodes (An elementary approach)

Cited by in corpus (1)

• Measuring the local non-convexity of real algebraic curves