Fanography

$\mathrm{Bl}_3\mathbb{P}^2$ $\mathrm{Bl}_5\mathbb{P}^2$

del Pezzo surface $\mathrm{Bl}_4\mathbb{P}^2$

Picard rank

5

$-\mathrm{K}_S^2$

5

alternatives

divisor of degree $(1,2)$ in $\mathbb{P}^1\times\mathbb{P}^2$

section of $\mathrm{Gr}(2,5)$ in $\mathbb{P}^9$ by a codimension 4 linear subspace

index

1

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

6

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

yes

number of moduli

0

Bott vanishing

holds

group	dimension
$\mathrm{Sym}_5$	0