Not Generic Cases in \({\mathbb {P}}^2\)

In this chapter, we consider for the first time geometrical objects not necessarily in general position. We start with zero-dimensional schemes and linear spaces: Points can have many zero coordinates, and linear spaces can intersect coordinate hyperplanes in dimension greater than the expected one. These facts force us to study all possible pathological behaviours that can occur when computing the Hadamard product of such varieties.