Let $p \in H^4(\mathbb{CP}^2)$ and $\ell \in H^2(\mathbb{CP}^2)$ be the cohomology classes Poincaré dual to a point and a line respectively.


**Question.** What is the Gromov-Witten invariant $\langle p, p, \ell\rangle\_{0, 1}$ counting degree $1$, genus $0$ curves in $\mathbb{CP}^2$?



Gromov-Witten invariant $\langle p, p, \ell\rangle_{0, 1}$ counting degree $1$, genus $0$ curves in $\mathbb{CP}^2$?
As Dan says, you can use the divisor equation:
$$\langle e\_{\alpha\_1}, \ldots, e\_{\alpha\_n}, \ell \rangle\_{g,d} = d\ \langle e\_{\alpha\_1}, \ldots, e\_{\alpha\_n} \rangle\_{g,d} $$
where the $e\_{\alpha\_i}$ are any cohomology classes of $\mathbb{CP}^2$, to reduce your invariant $\langle p,p,\ell \rangle\_{0,1}$ to $\langle p,p\rangle\_{0,1}$, the number of lines through two points.


