are homogeneous polynomials.

A [*standard determinantal*]{} scheme $S\subseteq{\mathbb{P}}^{n+1}$ of codimension $c$ is a scheme whose saturated ideal $I_S$ is standard determinantal.

A standard determinantal ideal $I$ is [*good determinantal*]{} if after performing invertible row operations on the matrix $M$ and then deleting a row, the ideal generated by the maximal minors of the $(t-1)\times (t+c-1)$ matrix obtained is standard determinantal (that is, it has height $c+1$). In particular, we formally include the possibility that $t=1$, i.e. a complete intersection is good determinantal.

A scheme $S$ is [*good determinantal*]{} if its saturated ideal $I_S$ is good determinantal.

Let $S$ be a standard determinantal scheme with defining matrix $M=(F_{ij})$. We assume without loss of generality that $M$ contains no invertible entries. Let ${\mathcal U}=(u_{ji})$ be the transposed of the matrix whose entries are the degrees of the entries of $M$. ${\mathcal U}$ is the [*degree matrix*]{} of $S$. We adopt the convention that the entries of ${\mathcal U}$ increase from right to left and from top to bottom: $u_{ji} \geq u_{lk}$ if $i\leq k$ and $j \geq l$. $S$ can be regarded as the degeneracy locus of a degree 0 morphism $$\varphi:\bigoplus_{i=1}^t
R(b_i){\longrightarrow}\bigoplus_{j=1}^{t+c-1} R(a_j).$$ Set $a_1\leq\ldots\leq a_{t+c-1}$ and $b_1\leq\ldots\leq b_t$. Then $\varphi$ 