# Fanography

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

Identification
##### Fano variety 2-36

$\mathbb{P}(\mathcal{O}_{\mathbb{P}^2}\oplus\mathcal{O}_{\mathbb{P}^2}(2))$

Picard rank
2 (others)
$-\mathrm{K}_X^3$
62
$\mathrm{h}^{1,2}(X)$
0
Hodge diamond
1
0 0
0 2 0
0 0 0 0
0 2 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
34
$-\mathrm{K}_X$ very ample?
yes
$-\mathrm{K}_X$ basepoint free?
yes
hyperelliptic
no
trigonal
no
Birational geometry

This variety is rational.

This variety is primitive.

This variety can be blown up (in a curve) to

• 3-9, in a curve of genus 3
• 3-14, in a curve of genus 1
• 3-22, in a curve of genus 0
Deformation theory
number of moduli
0

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$\mathrm{Aut}(\mathbb{P}(1,1,1,2))$ 15 0
Period sequence

The following period sequences are associated to this Fano 3-fold:

GRDB
#6
Fanosearch
#58
Toric geometry

This variety is toric.

It corresponds to ID #7 on grdb.co.uk.