Fanography

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

Identification

Fano variety 2-2

double cover of 2-34 with branch locus a $(2,4)$-divisor

rank
2 (others)
$-\mathrm{K}_X^3$
6
$\mathrm{h}^{1,2}(X)$
20
Hodge diamond
1
0 0
0 2 0
0 20 20 0
0 2 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
6
$-\mathrm{K}_X$ very ample?
no
$-\mathrm{K}_X$ basepoint free?
yes
hyperelliptic
yes
trigonal
no
Birational geometry

This variety is not rational but unirational.


This variety is primitive.

Deformation theory
number of moduli
33

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$0$ 0 33