Characteristic numbers of rational nodal curves in $\mathbb{P}^3$

TL;DR

This paper calculates the exact counts of rational nodal curves in three-dimensional projective space that satisfy specific incidence and tangency conditions, advancing enumerative geometry in algebraic geometry.

Contribution

It provides explicit formulas for the number of rational nodal curves in  passing through points, lines, and tangent to planes, a new result in enumerative geometry.

Findings

Derived explicit counts for rational nodal curves in 

Established methods for enumerating curves with singularities

Extended classical enumerative results to nodal cases

Abstract

In this paper we compute the number of rational curves with one node passing through a given number of points, lines and tangent to a given number of planes in $\mathbb{P}^3$.