Asymptotic of Enumerative Invariants in ${\mathbb {C}}P^2$

Abstract

In this paper, we give the asymptotic expansion of $n_{0,d}$ and $n_{1,d}$, where $(3d-1+g)!\, n_{g,d}$ counts the number of genus g curves in ${\mathbb {C}}P^2$ through $3d-1+g$ points in general position and can be identified with certain Gromov–Witten invariants.