Characteristic numbers of rational cuspidal space curves

TL;DR

This paper develops recursive formulas to compute characteristic numbers of rational space curves with a cusp, providing explicit formulas for low-dimensional cases and supporting numerical examples.

Contribution

It introduces effective recursive methods for calculating characteristic numbers of rational cuspidal space curves, including explicit formulas for ambient spaces up to dimension 5.

Findings

Recursive formulas for characteristic numbers

Explicit formulas for dimensions up to 5

Numerical examples demonstrating the methods

Abstract

We solve the problem of computing characteristic numbers of rational space curves with a cusp, where there may or may not be a condition on the node. The solution is given in the form of effective recursions. We give explicit formulas when the dimension of the ambient projective space is at most 5. Many numerical examples are provided. A C++ program implementing most of the recursions is available upon request