A remark on Gromov-Witten-Welschinger invariants of $\mathbb{C}{P}^3\#{\overline{\mathbb{C}P}}^3$

Abstract

We generalize the formula of Gromov-Witten-Welschinger invariants of $\mathbb{C}{P}^3$ established by E. Brugallé and P. Georgieva in [BG16b] to $\mathbb{C}{P}^3\#{\overline{\mathbb{C}P}}^3$. Using pencils of quadrics, some real and complex enumerative invariants of $\mathbb{C}{P}^3\#{\overline{\mathbb{C}P}}^3$ can be written as the combination of the enumerative invariants of the blow up of $\mathbb{C}{P}^2$ at two real points.

13 pages, 2 figures, comments are welcome