a generalized row of $M$, up to nonzero scalar multiples the $(d-1)\times (d-1)$ minors of the remaining rows are all the squarefree monomials of degree $d-1$ in $k[x_0,\ldots,x_n]$. Since they generate a standard determinantal ideal, $I$ is good determinantal.

In order for the result of Lemma \[sqfr\] to hold we do not even need the ground field $k$ to have infinite cardinality. However we need to have enough scalars in $k$ so that we can find a matrix $A$ of size $d\times (n+1)$ with entries in $k$ such that all the $d\times d$ minors of $A$ are nonzero. If $|k|\geq
d+1$ we can let $A$ be the Vandermonde matrix in $\alpha_1,\ldots,\alpha_d$, distinct elements in $k^*$, i.e. $a_{ij}=\alpha_i^{j-1}$.

The next proposition is a straightforward consequence of Lemma \[sqfr\].

\[genpts\] $n+1$ generic points in ${\mathbb{P}}^n$ are a good determinantal scheme.

Observe that $n+1$ generic points in ${\mathbb{P}}^n$ can be mapped via a change of coordinates to the $n+1$ coordinate points. The saturated ideal of the $n+1$ coordinate points in ${\mathbb{P}}^n$ is generated by the squarefree monomials of degree 2 in $x_0,\ldots,x_n$. Therefore it is a good determinantal scheme by Lemma \[sqfr\].

Let $C\subseteq{\mathbb{P}}^{n+1}$ be a nondegenerate, reduced and irreducible curve of degree 