del Pezzo surface: $\mathbb{P}^2$
Identification
$\mathbb{P}^1\times\mathbb{P}^1$
del Pezzo surface $\mathbb{P}^2$: projective plane
- Picard rank
- 1
- $-\mathrm{K}_S^2$
- 9
Hodge diamond
1
0 0
0 1 0
0 0
1
0 0
0 1 0
0 0
1
Anticanonical bundle
- index
- 3
- $\dim\mathrm{H}^0(S,\omega_S^\vee)$
- 10
- $-\mathrm{K}_S$ very ample?
- yes
Deformation theory
- number of moduli
- 0
- Bott vanishing
- holds
Automorphism groups
| group | dimension | |
| $\mathrm{PGL}_3$ | 8 |