Fanography

$\mathrm{Bl}_2\mathbb{P}^2$ $\mathrm{Bl}_4\mathbb{P}^2$

del Pezzo surface $\mathrm{Bl}_3\mathbb{P}^2$

Picard rank

4

$-\mathrm{K}_S^2$

6

alternatives

divisor of degree $(1,1,1)$ in $\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1$

complete intersection of two $(1,1)$-divisors in $\mathbb{P}^2\times\mathbb{P}^2$

index

1

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

7

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

yes

number of moduli

0

Bott vanishing

holds

group	dimension
$(\mathbb{G}_{\mathrm{m}}^2\rtimes\mathrm{Sym}_3)\times\mathrm{Sym}_2$	2