Fanography

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

del Pezzo surface: $\mathrm{Bl}_2\mathbb{P}^2$

Identification

del Pezzo surface $\mathrm{Bl}_2\mathbb{P}^2$
Picard rank
3
$-\mathrm{K}_S^2$
7
Hodge diamond
1
0 0
0 3 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(S,\omega_S^\vee)$
8
$-\mathrm{K}_S$ very ample?
yes
Deformation theory
number of moduli
0
Automorphism groups
group dimension
$\left\{ \Bigl( \begin{smallmatrix} 1 & 0 & * \\ 0 & * & * \\ 0 & 0 & * \end{smallmatrix} \Bigr) \right\}\rtimes\mathrm{Sym}_2$ 4