$P$. Then $Z$ is standard determinantal and a section of $C$ by a hyperplane that meets it properly. However, $Z$ is not good determinantal. In fact, deleting a generalized row we obtain the matrix of size $1\times 4$ $$\left(\begin{array}{cccc}
\alpha x_0 & (1+\alpha)x_1 & x_2 & x_0+x_1+\alpha x_2
\end{array}\right)$$ whose entries generate the ideal $(x_0,x_1,x_2)$ of codimension $3<4$.

.5cm Every standard determinantal scheme is arithmetically Cohen-Macaulay. Moreover, the two families coincide for schemes of codimension $1$ or $2$, while for codimension $3$ or higher the family of arithmetically Cohen-Macaulay schemes strictly contains the family of standard determinantal schemes. From the results in [@hu93] one can easily obtain a sufficient condition for a scheme $V\subseteq{\mathbb{P}}^{n+1}$ to be arithmetically Cohen-Macaulay in terms of the graded Betti numbers of a general hyperplane section of $V$. If a general hyperplane section of $V$ is standard determinantal, the condition can be expressed in terms of the entries of its degree matrix. Notice that since the graded Betti numbers of a hyperplane section of $V$ are the same for a general choice of the hyperplane, the degree matrix is also the same for a general choice of the hyperplane.

\[aCM\] Let $V\subseteq{\mathbb{P}}^{n+1}$ be a projective scheme. 