Identification
Hodge diamond
1
0 0
0 2 0
0 9 9 0
0 2 0
0 0
1
0 0
0 2 0
0 9 9 0
0 2 0
0 0
1
Anticanonical bundle
 index
 1
 $\dim\mathrm{H}^0(X,\omega_X^\vee)$
 9
 $\mathrm{K}_X$ 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.
This variety is fibrelike, i.e. it can appear as the fibre of a Mori fibre space.
Deformation theory
 number of moduli

 19
 18
$\mathrm{Aut}^0(X)$  $\dim\mathrm{Aut}^0(X)$  number of moduli 

$0$  0  19 