On Hadamard products of linear varieties

Abstract

In this paper, we address the Hadamard product of linear varieties not necessarily in general position. In [Formula: see text], we obtain a complete description of the possible outcomes. In particular, in the case of two disjoint finite sets [Formula: see text] and [Formula: see text] of collinear points, we get conditions for [Formula: see text] to be either a collinear finite set of points or a grid of [Formula: see text] points. In [Formula: see text] under suitable conditions (which we prove to be generic), we show that [Formula: see text] consists of [Formula: see text] points on the two different rulings of a nondegenerate quadric and we compute its Hilbert function in the case [Formula: see text]