A Remark on the Gromov–Witten–Welschinger Invariants of $${ℂP^3}\# {\overline {ℂP} ^{{3_*}}}$$

Abstract

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