Recursive Formulas for the Characteristic Numbers of Rational Plane Curves

TL;DR

This paper develops recursive formulas for counting rational plane curves with specific singularities and conditions, advancing enumerative geometry methods using techniques similar to quantum cohomology.

Contribution

It introduces recursive equations for characteristic numbers of rational nodal plane curves with at most one cusp, utilizing novel techniques related to quantum cohomology.

Findings

Derived recursive formulas for characteristic numbers

Extended methods to include curves with a cusp

Provided computational tools for enumerative geometry

Abstract

We derive recursive equations for the characteristic numbers of rational nodal plane curves with at most one cusp, subject to point conditions, tangent conditions and flag conditions, developing techniques akin to quantum cohomology on a moduli space of stable lifts.