Fanography

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

Identification

Fano variety 2-18

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

rank
2 (others)
$-\mathrm{K}_X^3$
24
$\mathrm{h}^{1,2}(X)$
2
Hodge diamond
1
0 0
0 2 0
0 2 2 0
0 2 0
0 0
1
Anticanonical bundle
index
1
$\dim\mathrm{H}^0(X,\omega_X^\vee)$
15
$-\mathrm{K}_X$ 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

  • 3-4, in a curve of genus 0
Deformation theory
number of moduli
6

$\mathrm{Aut}^0(X)$ $\dim\mathrm{Aut}^0(X)$ number of moduli
$0$ 0 6