Fanography

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

Identification

Fano variety 2-8
  1. double cover of 2-35 with branch locus an anticanonical divisor such that the intersection with the exceptional divisor is smooth
  2. double cover of 2-35 with branch locus an anticanonical divisor such that the intersection with the exceptional divisor is singular but reduced
rank
2 (others)
$-\mathrm{K}_X^3$
14
$\mathrm{h}^{1,2}(X)$
9
Hodge diamond
1
0 0
0 2 0
0 9 9 0
0 2 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
10
$-\mathrm{K}_X$ very ample?
yes
$-\mathrm{K}_X$ basepoint free?
yes
hyperelliptic
no
trigonal
no
Birational geometry

This variety is not rational but unirational.


This variety is primitive.

Deformation theory
number of moduli
  1. 18
  2. 17

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