Fanography

A tool to visually study the geography of Fano 3-folds.

del Pezzo surface: $\mathbb{P}^2$

Identification

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
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
Automorphism groups
group dimension
$\mathrm{PGL}_3$ 8