Pencils of quadrics and Gromov-Witten-Welschinger invariants of $\mathbb{C}{P}^3$

Abstract

We establish a formula for the Gromov-Witten-Welschinger invariants of $\mathbb{C}{P}^3$ with mixed real and conjugate point constraints. The method is based on a suggestion by J. Kollár that, considering pencils of quadrics, some real and complex enumerative invariants of $\mathbb{C}{P}^3$ could be computed in terms of enumerative invariants of $\mathbb{C}{P}^1\times \mathbb{C}{P}^1$ and of elliptic curves.

arXiv comment14 pages, 4 figures, minor corrections following referee's suggestions