Let $k$ be a field (if necessary algebraically closed), and $A,B$ are the same dimensional abelian varieties.
Now we consider their Kummer varieties $K_A:=A/\{\pm 1\}$ and $K_B$ which are algebraic varieties over $k$.
I want to know equivalent condition of $K_A\cong K_B$ for $A,B$.
In the case of $g=1$, Kummer line of elliptic curve is projective line. Especially, I want to know the case $g=2$.