Identification

##### Fano variety 10-1

$\mathbb{P}^1\times\mathrm{Bl}_8\mathbb{P}^2$

- Picard rank
- 10
- $-\mathrm{K}_X^3$
- 6
- $\mathrm{h}^{1,2}(X)$
- 0

Hodge diamond

1

0 0

0 10 0

0 0 0 0

0 10 0

0 0

1

0 0

0 10 0

0 0 0 0

0 10 0

0 0

1

Anticanonical bundle

- index
- 1
- $\dim\mathrm{H}^0(X,\omega_X^\vee)$
- 6
- $-\mathrm{K}_X$ very ample?
- no
- $-\mathrm{K}_X$ basepoint free?
- no
- hyperelliptic
- yes
- trigonal
- no

Birational geometry

Deformation theory

- number of moduli
- 8

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

$\mathrm{PGL}_2$ | 3 | 8 |

Period sequence

There is no period sequence associated to this Fano 3-fold.