Deformation of a singular CY manifold Let $X$ and $Y$ be generic cubic and quadric hypersurfaces in $\mathbb{CP}^4$. Let $Z$ be their intersection, which is a K3 surface. Then by adjunction formula, $N_{Z/X}=-K_X|_Z$ and $N_{Z/Y}=-K_Y|_Z$ are both ample. On the other hand, Kawamata-Namikawa deformation theorem claims that $X\cup Y$ is smoothable iff $N_{Z/X}\otimes N_{Z/Y} \cong \mathcal{O}_Z$. This should hold in our case because $X\cup Y$ is smoothable to a quintic threefold, but it conflicts with the above ampleness. So it seems I misunderstand something. Could anyone point it out? 
 A: Let me explain more concretely what's happening.
Choose a smooth quintic hypersurface $W$ in $\mathbb C \mathbb P^4$ that intersect transversely with $X \cap Y$. Then $W$ and $X+Y$ are linearly equivalent divisors.
Choose $\sigma, \sigma_0$ from $H^0(\mathbb C \mathbb P^4, \mathcal O_{\mathbb C \mathbb P^4}(W))$ such that
$$div(\sigma) = W, div(\sigma_0) = X+Y.$$
Let
$$\mathcal X = \{(x,t) \in {\mathbb C \mathbb P^4} \times \mathbb C | x \in div(\sigma_0 + t \sigma) \}$$
and let $\pi : \mathcal X \rightarrow \mathbb C$ be one of the projection.
Then
$$\mathcal X_0 = X' \cup Y'$$
and
$$\mathcal X_\infty = W',$$
where $\mathcal X_t = \pi^{-1}(t)$, $X'=X\times \{0\}$, $Y'=Y\times \{0\}$ and
$W'= W\times \{\infty\}$.
So it is smoothing of $X' \cup Y' \simeq X \cup Y $ to $W' \simeq W$.
But the total space $\mathcal X$ is not smooth and it has singularities along the smooth curve $C:=(X'\cap Y' \cap W') \times \{0 \}$. The singularities locally are the product of a smooth curve and a
three-dimensional ordinary double point singularity. If we blow up $\mathcal X$ along $C$, then
the exceptional locus is a $\mathbb C \mathbb P^1 \times \mathbb C \mathbb P^1 $-bundle over $C$. It is a usual procedure to contract
one of the ruling of the bundle smoothly to get $\mathcal X'$ and have another smoothing $ \mathcal X' \rightarrow \mathbb C$.
We can choose the ruling of the contraction such that
$$\mathcal X'_0 = X'' \cup Y''$$
where $X'' \simeq X'$ and $Y''$ is the blow-up of $Y'$ along $C$.
Now the total space $\mathcal X'$ is smooth. For the central fiber $X'' \cup Y''$, 
we have the $d$-semistable condition
$$N_{Z''/X''} \otimes N_{Z''/Y''} \simeq \mathcal O_{Z''},$$
where $Z'' = X'' \cap Y''$.
