Fanography

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

Identification

Fano variety 1-6

section of half-spinor embedding of a connected component of $\mathrm{OGr}_+(5,10)$ by codimension 7 subspace

rank
1 (others)
$-\mathrm{K}_X^3$
12
$\mathrm{h}^{1,2}(X)$
7
Hodge diamond
1
0 0
0 1 0
0 7 7 0
0 1 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
9
$-\mathrm{K}_X$ 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 is fibre-like, i.e. it can appear as the fibre of a Mori fibre space.

Deformation theory
number of moduli
18

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$0$ 0 18