Fanography

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

del Pezzo surface: $\mathrm{Bl}_8\mathbb{P}^2$

Identification

del Pezzo surface $\mathrm{Bl}_8\mathbb{P}^2$
Picard rank
9
$-\mathrm{K}_S^2$
1
Hodge diamond
1
0 0
0 9 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(S,\omega_S^\vee)$
2
$-\mathrm{K}_S$ very ample?
no, but $-3\mathrm{K}_S$ is
Deformation theory
number of moduli
8
Automorphism groups
type order structure
I 144
II 72
III 36
IV 30
V 24
VI 24
VII 24
VIII 20
IX 16
X 12
XI 12
XII 12
XIII 10
XIV 8
XV 8
XVI 8
XVII 6
XVIII 6
XIX 4
XX 4
XXI 2