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arXiv · 1606.08695

On Hadamard products of linear varieties

C. Bocci·G. Calussi·G. Fatabbi·A. Lorenzini
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Abstract

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'|.

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C. Bocci, G. Calussi, G. Fatabbi, A. Lorenzini. 2016-06-28. On Hadamard products of linear varieties. https://arxiv.org/abs/1606.08695

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