On Hadamard products of linear varieties
  In this paper we address the Hadamard product of linear varieties not necessarily in general position.   In $\mathbb{P}^2$ we obtain a complete description of the possible outcomes. In particular, in the case of two disjoint finite sets X and X' of collinear points, we get conditions for their hadamard product to be either a collinear finite set of points or a grid of | X|| X'| points.   In $\mathbb{P}^3,$ under suitable conditions (which we prove to be generic), we show that the hadamard product of X and X' consists of | X||X'| points on the two different rulings of a non-degenerate quadric and we compute its Hilbert function in the case |X| = |X'|. 
C. Bocci, G. Calussi, G. Fatabbi, A. Lorenzini
math.AG math.AC