P. Pastorino

On $\mathbb{P}^1$-bundles on $\mathbb{P}^3$ that are small modifications of a Fano fourfold

We find necessary conditions for the projectivization of a rank two vector bundle $\mathcal{E}$ on $\mathbb{P}^3_{\mathbb{C}}$ to be related to a smooth Fano 4-fold by a small $\mathbb{Q}$-factorial modification (SQM). Furthermore, we fully describe the birational geometry of $\mathbb{P}_{\mathbb{P}^3}(\mathcal{E})$ wh...