Identification

Hodge diamond

1

0 0

0 4 0

0 0 0 0

0 4 0

0 0

1

0 0

0 4 0

0 0 0 0

0 4 0

0 0

1

1

0 0

0 1 4

0 0 0 16

0 0 0

0 0

0

0 0

0 1 4

0 0 0 16

0 0 0

0 0

0

Anticanonical bundle

- index
- 1
- $\dim\mathrm{H}^0(X,\omega_X^\vee)$
- 16
- $-\mathrm{K}_X$ very ample?
- yes
- $-\mathrm{K}_X$ basepoint free?
- yes
- hyperelliptic
- no
- trigonal
- no

Birational geometry

Deformation theory

- number of moduli
- 1

$\mathrm{Aut}^0(X)$ | $\dim\mathrm{Aut}^0(X)$ | number of moduli |
---|---|---|

$\mathbb{G}_{\mathrm{m}}$ | 1 | 0 |

$0$ | 0 | 1 |

Period sequence

Extremal contractions

Semiorthogonal decompositions

A full exceptional collection can be constructed using Orlov's blowup formula.

Structure of quantum cohomology

Zero section description

Fano 3-folds from homogeneous vector bundles over Grassmannians gives the following description(s):

- variety
- $ \mathbb{P}^1_1 \times \mathbb{P}^1_2 \times \mathbb{P}^1_3 \times \mathbb{P}^4$
- bundle
- $\Lambda(0,0,0,1) \oplus \mathcal{O}(1,0,1,1)$

See the big table for more information.