observe that the good determinantal property does not behave as well as the standard determinantal property under hyperplane sections by a hyperplane that meets the scheme properly. In fact, any hyperplane section of a standard determinantal subscheme of ${\mathbb{P}}^{n+1}$ by a hyperplane that meets it properly is a standard determinantal subscheme of ${\mathbb{P}}^n$. It is not true in general that every hyperplane section of a good determinantal subscheme of ${\mathbb{P}}^{n+1}$ by a hyperplane that meets it properly is a good determinantal subscheme of ${\mathbb{P}}^n$. However, a general hyperplane section is good determinantal. Next, we see an example when this is the case. The following example was derived from Example 4.1 in [@kl01].

\[stgood\] Let $C\subseteq{\mathbb{P}}^4$ be a curve whose homogeneous saturated ideal is given by the maximal minors of $$\left(\begin{array}{cccc}
x_0 & x_1+x_4 & 0 & x_2 \\
0 & x_1 & x_2 & x_0+x_1
\end{array}\right).$$ One can check that $C$ is one-dimensional, hence standard determinantal. $C$ is a cone over a zero-dimensional scheme supported on the points $[0:0:0:1]$ and $[0:1:0:-1]$. The curve $C$ is indeed good determinantal, since deleting a generalized row we obtain the matrix of size $1\times 4$ $$\left(\begin{array}{cccc}
\alpha x_0 & (1+\alpha)x_1+\alpha x_4 & x_2 & 