x_1 & x_2 & x_3 & x_4 \end{array}\right).$$

.5cm Kleppe, Migliore, Miró-Roig, Nagel and Peterson proved that under certain assumptions the closure of the locus of good determinantal schemes with a fixed degree matrix $M$ is an irreducible component in the corresponding Hilbert scheme (see chapters 9 and 10 of [@kl01] and the paper [@kl05]). Clearly, standard determinantal schemes with the same degree matrix $\mathcal U$ belong to the closure of the locus of good determinantal ones. It is natural to ask whether a general ${t\choose 2}$-th hyperplane section of a scheme $V$ as in Proposition \[symm\] is standard (or good) determinantal. The following example shows that this is in general not the case.

\[verodeform\] Let $V\subseteq{\mathbb{P}}^9$ be the scheme whose saturated homogeneous ideal $I_V$ is generated by the submaximal minors of the matrix $$X=\left(
\begin{array}{cccc}
x_{0,0} & x_{0,1} & x_{0,2} & x_{0,3} \\
x_{0,1} & x_{1,1} & x_{1,2} & x_{1,3} \\
x_{0,2} & x_{1,2} & x_{2,2} & x_{2,3} \\
x_{0,3} & x_{1,3} & x_{2,3} & x_{3,3}
\end{array}\right).$$ In Proposition \[symm\] we showed that $V$ has a $3$-rd hyperplane section $C\subseteq{\mathbb{P}}^6$ that is good determinantal. More precisely, the ideal $I_C$ is generated by the maximal minors of the matrix $$Y=\left(\begin{array}{ccccc}
