2021/10/22 by Piene, Ragni, Riener, Cordian, Shapiro, Boris · 2 citations
#14H50 #51A50 #51M05 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2110.11691
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.