\vdots \\ 
x_{0,t-1} & x_{0,t} & x_{1,t} & x_{2,t} & \cdots & \cdots & \cdots & x_{t,t} 
\end{array}\right).$$ In fact, the maximal minors of $U$ coincide with the submaximal minors of $Y$. Moreover, the matrix $U$ is 1-generic. Therefore, the ideal of maximal minors of $U$ defines a reduced and irreducible, good determinantal scheme (see also Remark \[1gen\]).

Let $D$ be a general ${ {{t} \choose {2}} }$-th hyperplane section of $V$. The saturated ideal of $D$ is the ideal $I_D=I_t(Z)$ generated by the submaximal minors of the symmetric matrix $$Z=\left(\begin{array}{ccccc} 
x_{0,0} & x_{0,1} & \cdots & x_{0,t-1} & x_{0,t} \\ 
x_{0,1} & L_{1,1} & \cdots & L_{1,t-1} & x_{1,t} \\
\vdots & \vdots & & \vdots & \vdots \\
x_{0,t-1} & L_{1,t-1} & \cdots & L_{t-1,t-1} & x_{t-1,t} \\
x_{0,t} & x_{1,t} & \cdots & x_{t-1,t} & x_{t,t} \end{array}\right).$$ We can assume without loss of generality that the equations of the hyperplanes that we intersect with $V$ are $x_{i,j}-L_{i,j}$, $i\geq 1, j\leq t-1$, where $L_{i,j}$ is a general linear form in $k[x_{0,0},\ldots, x_{0,t},
x_{1,t},\ldots, x_{t,t}]$. Observe that we have a flat family of codimension 3 schemes $D_s$ whose saturated ideal is $I_t(Z_s)$, $Z_s=sZ+(1-s)Y$. In fact, for any choice of 