A Remark on the Gromov–Witten–Welschinger Invariants of $\mathbb{C} P^3\#\overline{\mathbb{C} P}^3$

We establish a formula for the Gromov–Witten–Welschinger invariants of $\mathbb{C} P^3\#\overline{\mathbb{C} P}^3$. Using birational transformations and pencils of quadrics, we write some real and complex enumerative invariants of $\mathbb{C} P^3\#\overline{\mathbb{C} P}^3$ as combinations of enumerative invariants of the blow up of $\mathbb{C} P^2$ at two real points.