an overview of the literature listing Fano fourfolds
Sols, I., Szurek, M., & Wiśniewski, J. A. (1991). Rank-2 Fano bundles over a smooth quadric Q₃. Pacific J. Math., 148(1), 153–159.
| count | 5 cases |
|---|---|
| construction | projective-bundle |
| Picard rank $\rho_X$ | 2 |
| entry numbering | case in Theorem 1 |
| invariants | construction |
| links | journal MR1091535 |
| notes | Complete classification of rank-2 Fano bundles over the 3-dimensional quadric Q₃ (5 cases); projectivizations are Fano fourfolds. |
Each row is a family from this source. The description column records the construction as given in the paper (ambient and defining bundle, Cox-ring data, base variety, or birational model, depending on the source); the invariant columns are those the paper tabulates. Provenance and conventions are noted below the table.
| entry | $\rho_X$ | description |
|---|---|---|
| SSW91:1 | 2 | $\mathcal{E}=\mathcal{O}\oplus\mathcal{O}(-1)$ over $Q_3$ ($c_1=-1$) |
| SSW91:2 | 2 | $\mathcal{E}=$ spinor bundle $\mathcal{E}_-$ over $Q_3$ ($c_1=-1$) |
| SSW91:3 | 2 | $\mathcal{E}=\mathcal{O}\oplus\mathcal{O}$ over $Q_3$ ($c_1=0$) |
| SSW91:4 | 2 | $\mathcal{E}=\mathcal{O}(-1)\oplus\mathcal{O}(1)$ over $Q_3$ ($c_1=0$) |
| SSW91:5 | 2 | $\mathcal{E}=$ stable rank-2 bundle on $Q_3$ with $c_1=0$, $c_2=2$ (pullback of a null-correlation bundle via a double cover $Q_3\to\mathbb{P}^3$) |
Bundle classification from Pacific J. Math. 148 (1991); P(E) is the Fano fourfold. No per-case numerical invariants are tabulated in the paper.