Higher Order Contact on Cayley's Ruled Cubic Surface

TL;DR

This paper investigates the complex contact properties of twisted cubics on Cayley's ruled cubic surface, exploring higher order contact and dual contact, and discusses related open problems in algebraic geometry.

Contribution

It provides new results and insights into higher order contact phenomena for twisted cubics on Cayley's surface, highlighting open problems in the field.

Findings

Analysis of higher order contact among twisted cubics

Results on dual contact of higher order

Identification of open problems in algebraic geometry

Abstract

It is well known that Cayley's ruled cubic surface carries a three-parameter family of twisted cubics sharing a common point, with the same tangent and the same osculating plane. We report on various results and open problems with respect to contact of higher order and dual contact of higher order for these curves.