Fanography

$\mathrm{Bl}_1\mathbb{P}^2$ $\mathrm{Bl}_3\mathbb{P}^2$

del Pezzo surface $\mathrm{Bl}_2\mathbb{P}^2$

Picard rank

3

$-\mathrm{K}_S^2$

7

alternatives

complete intersection of $(1,0,1)$- and $(0,1,1)$-divisor in $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^2$

index

1

$\dim\mathrm{H}^0(S,\omega_S^\vee)$

8

$-\mathrm{K}_S$ very ample?

yes

number of moduli

0

Bott vanishing

holds

group	dimension
$\left\{ \Bigl( \begin{smallmatrix} 1 & 0 & * \\ 0 & * & * \\ 0 & 0 & * \end{smallmatrix} \Bigr) \right\}\rtimes\mathrm{Sym}_2$	4