We construct via linkage a variety $X = X_{15} = X_{11} \cup X_{4} \subset \PP^7$, with Betti table
$\phantom{WWWW} \begin{matrix} &0&1&2&3&4\\\text{total:}&1&7&12&7&1\\\text{0:}&1&\text{.}&\text{.}&\text{.}&\text{.}\\\text{1:}&\text{.}&5&5&1&\text{.}\\\text{2:}&\text {.}&1&2&1&\text{.}\\\text{3:}&\text{.}&1&5&5&\text{.}\\\text{4:}&\text{.}&\text{.}&\text{.}&\text{.}&1\\ \end{matrix} $
For an artinian reduction $A_F$, the quadratic part of the ideal $F^\perp$ is the ideal of $\Gamma=\Gamma_4\cup p$, the union of a four points in a plane and one point outside. So we construct $X_{11}$ in the intersection of two quadrics in a P6 and $X_4$ in an independant P4. In the construction the intersection $X\cup X'$ of a component $X$ with the other is an anticanonical divisor on $X$.
We start with a linear $\mathbb{P}^3 \subset \mathbb{P}^7$, take the linked ideal via a $(1,2,2,3)$ complete intersection containing the $\mathbb{P}^3$.
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