the object of extensive study in commutative algebra. These families were studied from the geometric viewpoint by Kreuzer, Migliore, Nagel, and Peterson in [@kr00]. In this article, they introduced the definition of standard and good determinantal schemes that we use. The relevance of standard and good determinantal schemes in the context of liaison theory became clear in [@kl01], where it was shown that standard determinantal schemes belong to the Gorenstein-liaison class of a complete intersection.

In this note we study standard and good determinantal schemes and their general hyperplane sections. The property of being standard or good determinantal is preserved when taking a general hyperplane section. So we ask whether every arithmetically Cohen-Macaulay scheme whose general hyperplane section is good determinantal is itself good determinantal. The answer is negative. In Proposition \[symm\], Example \[vero\], and Proposition \[n+1curve\] we produce examples of schemes which are not standard determinantal, and whose general hyperplane section (or whose Artinian reduction) is good determinantal. We also show that a section of the schemes of Proposition \[symm\] by a number of generic hyperplanes is good determinantal up to flat deformation. Then we discuss the property of being standard or good determinantal in a flat family. This 