Consider a weighted projective space $\mathbb{P}_{a_1, \dotsc, a_r}$ and assume it is well-formed i.e. each $r-1$ of the $a_i$ are coprime. Let $g \in \mathbb{K}[T_1, \dotsc, T_r]$ be a weighted homogeneous polynomial and write $d := \deg(g)$. We call the hypersurface $X := V(g) \subseteq \mathbb{P}_{a_1, \dotsc, a_r}$ well-formed if $X$ does not contain any $2$-codimensional singular orbit of $\mathbb{P}_{a_1, \dotsc, a_r}$.
One of the standard references for weighted complete intersections is Iano-Fletcher. There 6.10 says that $X$ is well-formed if and only if $$ \gcd(a_i;\; i \neq i_1, i_2) \mid d $$ holds for all $1 \leq i_1 < i_2 \leq r$.
I don't see why this is true. For example, consider $\mathbb{P}_{1,1,4,6}$ and $g = T_1^2 + T_2^2 + T_1 T_2$. Let $Z$ be the torus orbit of $[0,0,1,1]$. Then $Z$ is 2-dimensional singular orbit due to $\gcd(4,6) = 2 \neq 1$. However we have $Z \subseteq X$ because $g$ depends only on the first to variables.
Could you give me a reference for a proof and/or a hint what I'm doing wrong?