Identification
Fano variety 223
 blowup of 116 in an intersection of $A\in\mathcal{O}_Q(1)$ and $B\in\mathcal{O}_Q(2)$ such that $A$ is smooth
 blowup of 116 in an intersection of $A\in\mathcal{O}_Q(1)$ and $B\in\mathcal{O}_Q(2)$ such that $A$ is singular
 Picard rank
 2 (others)
 $\mathrm{K}_X^3$
 30
 $\mathrm{h}^{1,2}(X)$
 1
Hodge diamond
1
0 0
0 2 0
0 1 1 0
0 2 0
0 0
1
0 0
0 2 0
0 1 1 0
0 2 0
0 0
1
Anticanonical bundle
 index
 1
 $\dim\mathrm{H}^0(X,\omega_X^\vee)$
 18
 $\mathrm{K}_X$ very ample?
 yes
 $\mathrm{K}_X$ basepoint free?
 yes
 hyperelliptic
 no
 trigonal
 no
Birational geometry
Deformation theory
 number of moduli

 2
 1
$\mathrm{Aut}^0(X)$  $\dim\mathrm{Aut}^0(X)$  number of moduli 

$0$  0  2 