but their general hyperplane sections are good determinantal.

Standard and good determinantal schemes
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Let $S$ be a scheme in ${\mathbb{P}}^{n+1}={\mathbb{P}}^{n+1}_k$, where $k$ is an algebraically closed field. Let $I_S$ be the saturated homogeneous ideal corresponding to $S$ in the polynomial ring $R=k[x_0,\ldots,x_{n+1}]$. We denote by ${\mathfrak{m}}$ the homogeneous irrelevant maximal ideal of $R$, ${\mathfrak{m}}=(x_0,\ldots ,x_{n+1})$. For a sheaf ${\mathcal{F}}$ we denote by $$H^i_*({\mathcal{F}})=\bigoplus_{m\in{\mathbb{Z}}}H^i({\mathbb{P}}^{n+1},{\mathcal{F}}(m))$$ the i-th cohomology ring. We will usually be interested in the case when ${\mathcal{F}}$ is an ideal sheaf. Let $T$ be a scheme that contains $S$. We denote by ${\mathcal{I}}_{S|T}$ the ideal sheaf of $S$ restricted to $T$, and by $I_{S|T}=H^0_*({\mathcal{I}}_{S|T})$ the ideal of $S$ restricted to $T$. We often write aCM for arithmetically Cohen-Macaulay.

In this note we study schemes whose general hyperplane section is standard or good determinantal. The following definition was given in [@kr00] for schemes, i.e. for saturated ideals. Here we extend it to include Artinian ideals.

\[stdef\] An ideal $I\subseteq k[x_0,\ldots,x_{n+1}]$ of height $c$ is [*standard determinantal*]{} if it is generated by the maximal minors of a homogeneous matrix $M$ of polynomials of size $t\times (t+c-1)$, for some $t\geq 1$. A matrix $M$ with polynomial entries is [*homogeneous*]{} if its minors 