Apocryphal Classes

In this chapter one surveys a few exceptional situations not fitting the known classes. There is an effort to collect some of these examples into plausible classes along with basic properties they enjoy as such. Some of these will involve a mixing of types of linear sections making the contents quite anomalous as compared to previous sufficiently well-behaved classes. An additional feature is the idea of looking at the properties of certain intermediate stages as when a linear section gradually degenerates into another – the case of the generic symmetric matrix and its Hankel like degeneration treated with some detail. By and large, the material is conjectural, while quite a bit of the examples resort to computer assistance. In spite of this, it is the hope that this survey like chapter will stimulate the interested reader that has thus far copped with the book contents.