# Fanography

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

Identification
##### Fano variety 2-24

divisor on $\mathbb{P}^2\times\mathbb{P}^2$ of bidegree $(1,2)$

rank
2 (others)
$-\mathrm{K}_X^3$
30
$\mathrm{h}^{1,2}(X)$
0
Hodge diamond
1
0 0
0 2 0
0 0 0 0
0 2 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
18
$-\mathrm{K}_X$ 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

• 3-8, in a curve of genus 0
Deformation theory
number of moduli
1

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$\mathbb{G}_{\mathrm{m}}^2$ 2 0
$\mathbb{G}_{\mathrm{m}}$ 1 0
$0$ 0 1