We construct via linkage an arithmetically Gorenstein 3-fold $X = X_{10} \cup X_{6} \subset \bf{P}^7$, of degree 16, having Betti table of type [430]. For an artinian reduction $A_F$, the quadratic part of the ideal $F^\perp$ is the ideal of a line and three independant points $p_1,p_2,p_3$, and $F^\perp$ contains pencils of ideals of three points on the line and the three fixed points $p_i$. In the pencil we find an ideal of four points in a plane and two on an independant line passing though one of the four points. We construct $X_{10}$ in a pencil of quadrics in a P6, and $X_{6}$ as a complete intersection in a P5. In the construction the intersection $X\cup X'$ of a component $X$ with the other is an anticanonical divisor on $X$.
The Betti table is $\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{.}&4&3&\text{.}&\text{.}\\ \text{2:}&\text{.}&3&6&3&\text{.}\\ \text{3:}&\text{.}&\text{.}&3&4&\text{.}\\ \text{4:}&\text{.}&\text{.}&\text{.}&\text{.}&1\\ \end{matrix} $
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