Return of the plane evolute

Abstract: Below we consider the evolutes of plane real-algebraic curves and discuss some of their complex and real-algebraic properties. In particular, for a given degree d ≥ 2, we provide lower bounds for the following four numerical invariants: 1) the maximal number of times a real line can intersect the evolute of a real-algebraic curve of degree d; 2) the maximal number of real cusps which can occur on the evolute of a real-algebraic curve of degree d; 3) the maximal number of (cru)nodes which can occur on the dual curve to the evolute of a real-algebraic curve of degree d; 4) the maximal number of (cru)nodes which can occur on the evolute of a real-algebraic curve of degree d.

differential geometrygeneral mathematicsgeneral topologygroup theorysymplectic geometry

Audience: researchers in the topic

Workshop on Singularity Theory, Geometry and Related Topics

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