On classifications of rational sextic curves

Identification of Planar Sextic Pythagorean-Hodograph Curves

Pythagorean-hodograph (PH) curves offer computational advantages in Computer Aided Geometric Design, Computer Aided Design, Computer Graphics, Computer Numerical Control machining and similar applications. In this paper, three methods are utilized to construct the identifications of planar regular sextic PH curves. The first exhibits purely the control polygon legs’ constraints in the complex f...

Cremona Transformations with an Invariant Rational Sextic

I t is well known that a Cremona transformation T with ten or fewer jF-points will transform a rational sextic S into a rational sextic S' when the F-points of T are all located at the nodes of S. I have shown (cf. [ l ] , p. 248, (9); [2], p. 255, (5)) that, even though the number of transformations T of the type indicated is infinite, the transforms S' are all included in 2 • 31 -51 classes, ...

On the rational monodromy - free potentials with sextic growth

We study the rational potentials V (x), with sextic growth at infinity , such that the corresponding one-dimensional Schrödinger equation has no monodromy in the complex domain for all values of the spectral parameter. We investigate in detail the subclass of such potentials which can be constructed by the Darboux transformations from the well-known class of quasi-exactly solvable potentials V ...

Rational Curves on Varieties

Rational points on curves