Identification
Fano variety 28
 double cover of 235 with branch locus an anticanonical divisor such that the intersection with the exceptional divisor is smooth
 double cover of 235 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
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

 18
 17
$\mathrm{Aut}^0(X)$  $\dim\mathrm{Aut}^0(X)$  number of moduli 

$0$  0  18 